An Online Parameter Estimation Using Current Injection with Intelligent Current-Loop Control for IPMSM Drives

Abstract

An online parameter estimation methodology using the d-axis current injection, which can estimate the distorted voltage of the current-controlled voltage source inverter (CCVSI), the varying dq-axis inductances, and the rotor flux, is proposed in this study for interior permanent magnet synchronous motor (IPMSM) drives in the constant torque region. First, a d-axis current injection-based parameter estimation methodology considering the nonlinearity of a CCVSI is proposed. Then, during current injection, a simple linear model is developed to model the cross- and self-saturation of the dq-axis inductances. Since the d-axis unsaturated inductance is difficult to obtain by merely using the recursive least square (RLS) method, a novel tuning method for the d-axis unsaturated inductance is proposed by using the theory of the maximum torque per ampere (MTPA) with the combination of the RLS method. Moreover, to improve the bandwidth of the current loop, an intelligent proportional-integral-derivative (PID) neural network controller with improved online learning algorithm is adopted to replace the traditional PI controller. The estimated the dq-axis inductances and the rotor flux are adopted in the decoupled control of the current loops. Finally, the experimental results at various operating conditions of the IPMSM in the constant torque region are given.

1. Introduction

There are many attractive benefits of the interior permanent magnet synchronous motors (IPMSMs), including the high-power density, high acceleration capability and broad speed operating range. Therefore, IPMSMs have been widely used in industries and transportations [1]. Nevertheless, the internal system parameter variations and unmodeled dynamics resulting from magnetic saturation, especially the inductances of the IPMSMs, will induce time-varying and nonlinear control characteristics of the IPMSMs. Thus, the development of parameter estimation techniques is significant to achieve reliable and high-precision field-oriented control performance for the IPMSMs [2,3,4,5,6,7,8].

According to the process of parameter estimation, the methods of parameter estimation can be mainly divided into two categories, the offline parameter estimation [2,3] and the online parameter estimation [4,5,6,7,8]. Generally, the offline methods demand a large amount of resources. The analyses of large quantities of data for different frequencies, voltages or currents are also necessary. Moreover, the variations of the dq-axis inductances with different load current and magnetic saturation can only be employed by using lookup tables. On the other hand, several online parameter estimation techniques have been developed to overcome the difficulties of the offline methods, and can obtain the machine parameters without using the lookup tables [4,5,6,7,8,9], and which can be further divided into the non-intrusive methods without signal injection [4,5,6] and the intrusive methods with signal injection [7,8,9]. A parameter estimation method composed of two affine projection algorithms (APAs) was proposed in [4]. Furthermore, two recursive least square (RLS) algorithms have been developed and employed the dynamic model of the machine in the dq reference frame in [5]. In addition, a method using the derivatives of the measured dc-bus voltage and stator current of the inverter during each PWM cycle to estimate machine inductances was introduced in [6]. However, estimating the parameters by using two RLS algorithms or APA is not straightforward, and improper estimation convergence is possible owing to measuring errors. Regarding the online parameter estimation strategies with signal injection, a current injection-based methodology considering the VSI nonlinearity and magnetic saturation has been introduced in [7]. Additionally, based on self-adaptive step size APA, using square-wave current injection was proposed in [8] for online parameter estimation. The disadvantage of the online parameter estimation methods using the injection signal is that the injected signals could increase the current and torque ripples and result in the deterioration of the control performance of motor drives. Nevertheless, the merits of the signal injection are easy implementation and no need for the addition of extra hardware devices [9].

In a field-oriented control (FOC) IPMSM, the effectiveness of the decoupled control the current-controlled voltage source inverter (CCVSI) depends on the correct values of the machine parameters. However, the machine parameters will vary due to magnetic saturation. Therefore, an online parameter estimation methodology using d-axis current injection is proposed for the IPMSM in the constant torque region. The smoothing values of dq-axis voltages, currents and electrical rotor speed are employed for the estimation. The above method can effectively eliminate the influence of measuring errors of voltages, currents and rotor position on estimation. Moreover, the proposed parameter estimation method can estimate the distorted voltage of the CCVSI, the varying dq-axis inductances and the rotor flux real time. Since the simplified inductance model proposed in [7] will result in inaccurate unsaturated inductance estimation, a new methodology of estimating the unsaturated inductance using the maximum torque per ampere (MTPA) theory combining with the RLS algorithm is proposed in this study. Furthermore, to shorten the estimation time, the distorted voltage is estimated by an analytical equation. In addition, the injected d-axis current is elaborately devised to reduce the influence on the control performance of the IPMSM drives. The estimation algorithms are developed deliberately to accomplish a straightforward flowchart which can ease the effort of practical implementation.

Since the MTPA control can improve the torque output in the constant torque region of an IPMSM, there are some published methods of MTPA in recent years [10,11,12,13,14]. In [10], a fuzzy control system adopting the high-frequency mechanical power change information was developed to acquire the advance angle for the MTPA scheme of an IPMSM. In [11], a small virtual current angle signal was injected to produce the d-axis current demand as well as to follow the MTPA operation point with the adoption of the internal properties of the MTPA. Moreover, in [12], a novel MTPA algorithm does not make use of any equations and motor parameters were proposed. In order to minimize the magnitude of the stator current vector at the given load torque, the current phase is varied continuously. In [13], a constant parameter MTPA strategy was proposed to control the permanent magnet-assisted synchronous reluctance motors. In addition, the machine learning approach was used to design the MTPA and flux-weakening control for an IPMSM in [14]. The d-axis current command can be varied downward gradually as proposed in [14] to find the lowest value of the stator current at a specific operating condition, i.e., the MTPA operating point which could satisfy that specific operating condition. Therefore, the MTPA method proposed in [14] is adopted in this study to find the lowest value of the stator current at a specific operating condition.

Since the control performance of the outer velocity loop or position loop is dependent on current regulation, the design of the bandwidth of the inner current loop is important [15]. In the digital control alternative current (AC) servo system, the bandwidth of current loop depends on switching frequency, plant parameters and the delay times, including sampling, pulse width modulation (PWM), filter, and calculation. Several approaches have been developed to enhance the bandwidth of current loop or current control ability of the permanent magnet synchronous motor (PMSM) drives [16,17,18,19,20]. These methods can improve the control performance, transient response, and robustness against machine parameter variations. Moreover, intelligent controllers using various neural networks are very effective to improve the robustness and performance of the synchronous motor drives due to their online learning, generalization, and parallel processing control characteristics [21,22]. Therefore, to improve the control performance and bandwidth of the current loop of the IPMSM drives, an intelligent proportional-integral-derivative (PID) neural network controller proposed in [23], with improved online learning algorithm, is developed in this study to replace the traditional PI controller for the current-loop control. Furthermore, the estimated dq-axis inductances and magnetic flux of the rotor are adopted in the decoupled control of the current loops to assure the effectiveness of the FOC IPMSM drive.

The rest of this study is organized as follows. In Section 2, first, a voltage model of IPMSM based on d-axis current injection considering the nonlinearity of a CCVSI is proposed. Second, the online estimation of the CCVSI distorted voltage is derived. In Section 3, during current injection, a simple linear model is developed to model the cross- and self-saturation of the dq-axis inductances. Then, the parameters of the linear model are estimated by using the RLS method. Moreover, the tuning method for the d-axis unsaturated inductance is proposed by using the theory of the MTPA with the combination of the RLS method. In Section 4, the estimated dq-axis inductances and magnetic flux of the rotor are then adopted in the decoupled control of the current-loop control. Furthermore, the intelligent PID neural network controller is employed to improve the control performance and bandwidth of the current loop. In addition, various operating conditions are investigated to verify the effectiveness of the proposed online parameter estimation methodology and the bandwidth improvement of current loop using the intelligent PID neural network controller in Section 5. Finally, some conclusions are presented in Section 6.

2. Online Parameter Estimation Using d-Axis Current Injection

2.1. Voltage Model of IPMSM Based on d-Axis Current Injection

An FOC IPMSM servo drive by using a space vector pulse width modulation (SVPWM) CCVSI with d-axis current injection is shown in Figure 1, including dq-axis current loops, voltage decoupled control and coordinate transformation. In Figure 1, $i_a$, $i_b$ and $i_c$ represent the three-phase currents; $v_{\alpha }$ and $v_{\beta }$ represent the voltage components in the stationary frame; $i_{\alpha }$ and $i_{\beta }$ represent the current components in the stationary frame; $v_d$ and $v_q$ represent the d-axis and q-axis stator voltages; $i_d$ and $i_q$ represent the d-axis and q-axis stator currents; $L_d$ and $L_q$ represent the d-axis and q-axis inductances; ${\lambda }_m$ is the magnetic flux of the rotor; ${\omega }_r$ represents the mechanical rotor speed; ${\theta }_r$ is the mechanical rotor position; $P$ denotes the number of poles; ${\theta }_e$ is the flux position the permanent magnet of the rotor; and the superscript * represents the reference value. Moreover, the effectiveness of the decoupled control depends on the online estimation of the dq-axis inductances and magnetic flux of the rotor by using the d-axis current injection method.

The implementation of the d-axis current injection is shown in Figure 2. First, when the IPMSM reaches the steady state, where $\mathsf{\Delta }{i}_{d1}=0$, the measured dq-axis voltages, currents and electrical rotor speed for the time of one electrical cycle $T_1$ are collected. Then, two perturbations in d-axis reference currents with $\mathsf{\Delta }{i}_{d2}=-1\mathrm{A}$ and $\mathsf{\Delta }{i}_{d3}=-2\mathrm{A}$ are injected one after the other into the IPMSM drive. To ensure the steady state is reached, the measurement data are only collected for each event after 5 ms. The measuring time for the other two perturbations in d-axis reference currents are $T_2$ and $T_3$, which are also the time of one electrical cycle of the motor drive. The proposed scheme of the injected d-axis current can reduce the influence of the control performance of the IPMSM drives owing to the very short duration of current injection. After measuring, the estimation of the CCVSI distorted voltage term and IPMSM parameters is performed.

The voltage model with d-axis current injection at steady state of an IPMSM in the dq reference frame can be expressed as follows:

$$V_{di}=R{i}_{di}-{\omega }_{ei}{L}_{qi}{i}_{qi}$$

(1)

$$V_{qi}=R{i}_{qi}+{\omega }_{ei}{L}_{di}{i}_{di}+{\omega }_{ei}{\lambda }_m i=1,2,3$$

(2)

where R is resistance of stator winding; ${\omega }_e$ is electrical rotor speed; subscript i indicates three steady states. Furthermore, the CCVSI nonlinearity, which is generally caused by the switching periods, voltage drops of the power devices and the dead-time effects, is also considered in the voltage model. Hence, the parameters R and ${\lambda }_m$ are assumed to be constant due to the short time step of the current injection. The dq-axis circuit model with the CCVSI nonlinearity is presented in Figure 3, where ϕ represents the voltage vector angle referred to the q-axis; $V_{dead}$ and V indicate the distorted voltages; $r_{cd}$ is the equivalent resistance [24]. In addition, the distorted parameters $D_d$ and $D_q$ are periodic functions of the rotor position ${\theta }_r$ and the current angle γ as follows [24]:

$$D_d=2\sin [{\theta }_r-\mathrm{int}\{\frac{3({\theta }_r+\gamma +\frac{\pi }{6})}{\pi }\}\times \frac{\pi }{3}]$$

(3)

$$D_q=2\cos [{\theta }_r-\mathrm{int}\{\frac{3({\theta }_r+\gamma +\frac{\pi }{6})}{\pi }\}\times \frac{\pi }{3}]$$

(4)

where the current angle γ is the angle between the current vector and q-axis. Since $r_{cd}$ can be included in R and $V_{dead}$ is much larger than V, the voltage model considering the nonlinearity of a CCVSI for an IPMSM in the dq reference frame can be expressed as follows:

$$V_{di}^{*}=R{i}_{di}-{\omega }_{ei}{L}_{qi}{i}_{qi}+D_{di}{V}_{dead}$$

(5)

$$V_{qi}^{*}=R{i}_{qi}+{\omega }_{ei}{L}_{di}{i}_{di}+{\omega }_{ei}{\lambda }_m+D_{qi}{V}_{dead} i=1,2,3$$

(6)

The smoothing values of dq-axis voltages ${\overline{V}}_{dq}^{*}$, currents ${\overline{i}}_{dq}$ and electrical rotor speed ${\overline{\omega }}_e$ are obtained from (7) as follows:

$${\overline{V}}_{dq}^{*}=\frac{1}{N}{\displaystyle \sum _{k=1}^N{V}_{dq}^{*}}(k), {\overline{i}}_{dq}=\frac{1}{N}{\displaystyle \sum _{k=1}^N{i}_{dq}}(k), {\overline{\omega }}_{\mathrm{e}}=\frac{1}{N}{\displaystyle \sum _{k=1}^N{\omega }_e}(k)$$

(7)

In (7), the smoothing values of each electrical cycle are adopted in the parameter estimation where $N=T_i/T_s$; $T_i$ is one electrical cycle time; $T_s$ is sampling time. Additionally, the smoothing values of the distorted coefficients $D_d$ and $D_q$, i.e., ${\overline{D}}_{di}$ and ${\overline{D}}_{qi}$, are as follows [7]:

$${\overline{D}}_{di}=\frac{1}{N^{\prime }}{\displaystyle \sum _{k=1}^{N^{\prime }}2\sin [{\theta }_{rk}-\mathrm{int}\{\frac{3({\theta }_{rk}+{\gamma }_i+\frac{\pi }{6})}{\pi }\}\times \frac{\pi }{3}]}$$

(8)

$${\overline{D}}_{qi}=\frac{1}{N^{\prime }}{\displaystyle \sum _{k=1}^{N^{\prime }}2\cos [{\theta }_{rk}-\mathrm{int}\{\frac{3({\theta }_{rk}+{\gamma }_i+\frac{\pi }{6})}{\pi }\}\times \frac{\pi }{3}]}$$

(9)

where $N^{\prime }=360$ for 360 electrical degrees, and ${\overline{D}}_{di}$ and ${\overline{D}}_{qi}$ are constants at steady state. It can be seen from (8), (9) that ${\overline{D}}_{di}$ and ${\overline{D}}_{qi}$ are only functions of the current angle ${\gamma }_i$ and are independent of rotor position owing to the average of the data of one mechanical cycle. Substituting (7)–(9) into (5) and (6), one can obtain:

$${\overline{V}}_{di}^{*}=R{\overline{i}}_{di}-{\overline{\omega }}_{ei}{L}_{qi}{\overline{i}}_{qi}+{\overline{D}}_{di}{V}_{dead}$$

(10)

$${\overline{V}}_{qi}^{*}=R{\overline{i}}_{qi}+{\overline{\omega }}_{ei}{L}_{di}{\overline{i}}_{di}+{\overline{\omega }}_{ei}{\lambda }_m+{\overline{D}}_{qi}{V}_{dead}$$

(11)

2.2. Estimation of Distorted Voltage Term $V_{dead}$

In this study, the distorted voltage term $V_{dead}$ is estimated by using the known stator winding resistance R in the following derivation. The following equation can be obtained by multiplying (10) by $i_d$ and multiplying (11) by $i_q$ and adding together:

$${\overline{V}}_{di}^{*}{\overline{i}}_{di}+{\overline{V}}_{qi}^{*}{\overline{i}}_{qi}=R({\overline{i}}_{di}^2+{\overline{i}}_{qi}^2)+{\overline{\omega }}_{ei}[(L_{di}-L_{qi}){\overline{i}}_{qi}{\overline{i}}_{di}+{\lambda }_m{\overline{i}}_{qi}]+{\widehat{V}}_{dead}({\overline{D}}_{di}{\overline{i}}_{di}+{\overline{D}}_{qi}{\overline{i}}_{qi})$$

(12)

Moreover, substituting $[(L_{di}-L_{qi}){\overline{i}}_{qi}{\overline{i}}_{di}+{\lambda }_m{\overline{i}}_{qi}]=T_{ei}\times \frac{4}{3P}=\frac{T_{ei}}{6}$ to (12) and P = 8 results in the following equation:

$${\overline{V}}_{di}^{*}{\overline{i}}_{di}+{\overline{V}}_{qi}^{*}{\overline{i}}_{qi}=R({\overline{i}}_{di}^2+{\overline{i}}_{qi}^2)+{\overline{\omega }}_{ei}\frac{T_{ei}}{6}+{\widehat{V}}_{dead}({\overline{D}}_{di}{\overline{i}}_{di}+{\overline{D}}_{qi}{\overline{i}}_{qi})$$

(13)

Thus, the distorted voltage term $V_{dead}$ can be estimated as follows:

$${\widehat{V}}_{deadi}=\frac{{\overline{V}}_{di}^{*}{\overline{i}}_{di}+{\overline{V}}_{qi}^{*}{\overline{i}}_{qi}-R({\overline{i}}_{di}^2+{\overline{i}}_{qi}^2)-{\overline{\omega }}_{ei}\frac{T_{ei}}{6}}{({\overline{D}}_{di}{\overline{i}}_{di}+{\overline{D}}_{qi}{\overline{i}}_{qi})}$$

(14)

Then, (10) and (11) can be represented by (15) and (16) as follows:

$${\overline{V}}_{di}^{*}=R{\overline{i}}_{di}-{\overline{\omega }}_{ei}{L}_{qi}{\overline{i}}_{qi}+{\overline{D}}_{di}{\widehat{V}}_{deadi}$$

(15)

$${\overline{V}}_{qi}^{*}=R{\overline{i}}_{qi}+{\overline{\omega }}_{ei}{L}_{di}{\overline{i}}_{di}+{\overline{\omega }}_{ei}{\lambda }_m+{\overline{D}}_{qi}{\widehat{V}}_{deadi}$$

(16)

The q-axis inductance $L_{qi}$ can be obtained directly by using (15). However, since the number of parameters to be estimated is higher than the rank of (16), it is unable to estimate the d-axis inductance $L_{di}$ and the rotor flux ${\lambda }_m$ directly from (16). Therefore, the RLS algorithm is adopted to solve the difficulty.

3. RLS Parameter Estimation Methodology

The cross-saturation effect is much smaller than the self-saturation effect owing to the small magnitude of injected d-axis currents. Therefore, one can assume the cross-saturation to be zero in order to simplify the estimation in practical implementation. Thus, during current injection, the linear Equations (17) and (18) are adopted to model the self-saturation of dq-axis inductances as follows:

$$L_q=L_{q0}-{\beta }_q{i}_q$$

(17)

$$L_d=L_{d0}-{\beta }_d{i}_d$$

(18)

where $L_{d0}$ and $L_{q0}$ are the d-axis and q-axis unsaturated inductances; ${\beta }_d$ and ${\beta }_q$ are the d-axis and q-axis self-saturation constants. Substituting (17) and (18) into (15) and (16), the following equations can be obtained:

$${\overline{V}}_{di}^{*}-R{\overline{i}}_{di}-{\overline{D}}_{di}{\widehat{V}}_{deadi}=-{\overline{\omega }}_{ei}(L_{q0}{\overline{i}}_{qi}-{\beta }_q{\overline{i}}_{qi}^2)$$

(19)

$${\overline{V}}_{qi}^{*}-R{\overline{i}}_{qi}-{\overline{D}}_{qi}{\widehat{V}}_{deadi}={\overline{\omega }}_{ei}(L_{d0}{\overline{i}}_{di}-{\beta }_d{\overline{i}}_{di}^2+{\lambda }_m)$$

(20)

The adopted RLS algorithm is listed in (21) as follows:

$$\begin{array}{l}{y}_k={\mathrm{\Phi }}_k^T{x}_k\\ {\widehat{x}}_{k+1}={\widehat{x}}_k+G_{k+1}[y_{k+1}-{\mathrm{\Phi }}_{k+1}^T{\widehat{x}}_k]\\ G_{k+1}=P_k{\mathrm{\Phi }}_{k+1}{[1+{\mathrm{\Phi }}_{k+1}^T{P}_k{\mathrm{\Phi }}_{k+1}]}^{-1}\\ P_{k+1}=P_k-G_{k+1}{\mathrm{\Phi }}_{k+1}^T{P}_k\end{array}$$

(21)

where subscript k is the number of iterations; $y_k$ and ${\mathrm{\Phi }}_k^T$ are known model parameters and $x_k$ is the model parameters to be estimated, which are depicted as follows:

$$\begin{array}{l}x={[{\beta }_d {\widehat{\lambda }}_m]}^{\mathrm{T}}, \mathrm{\Phi }=\left[\begin{array}{cc}-{\overline{\omega }}_{e2}{\overline{i}}_{d2}^2& {\overline{\omega }}_{e2}\\ -{\overline{\omega }}_{e3}{\overline{i}}_{d3}^2& {\overline{\omega }}_{e3}\end{array}\right]\\ y=\left[\begin{array}{c}{\overline{V}}_{q2}^{*}-R{\overline{i}}_{q2}-{\overline{D}}_{q2}{\hat{V}}_{\mathit{dead}2}-{\overline{\omega }}_{e2}{L}_{d0}{\overline{i}}_{d2}\\ {\overline{V}}_{q3}^{*}-R{\overline{i}}_{q3}-{\overline{D}}_{q3}{\hat{V}}_{\mathit{dead}3}-{\overline{\omega }}_{e3}{L}_{d0}{\overline{i}}_{d3}\end{array}\right] \end{array}$$

(22)

Additionally, ${\beta }_d, {\widehat{\lambda }}_m$ can be estimated by using the 2nd order RLS algorithm. Since the d-axis unsaturated inductance $L_{d0}$ is difficult to obtain by merely using the RLS, a novel tuning method for the d-axis unsaturated inductance is proposed by using the theory of the MTPA. The lowest value of the stator current, i.e., the MTPA operating point which could satisfy a specific operating condition in terms of speed and load torque, could be obtained by varying the d-axis current command gradually [14]. The resulted d-axis current which can lead to the lowest value of the stator current is defined as $i_{d,MTPA}^{*}$. Moreover, the electromagnetic torque equation is differentiated with respect to the q-axis current and the derivative is set to zero. Then, the extreme value can be obtained, and resulted in the d-axis current command of MTPA as follows [14]:

$$i_{d,MTPA}^{*\prime }=\frac{-{\widehat{\lambda }}_m+\sqrt{{\widehat{\lambda }}_m^2+4{({\widehat{L}}_d-{\widehat{L}}_q)}^2{\overline{i}}_q^2}}{2({\widehat{L}}_d-{\widehat{L}}_q)}$$

(23)

where $i_{d,MTPA}^{*\prime }$ is the estimated value of $i_{d,MTPA}^{*}$ by using ${\widehat{L}}_q, {\widehat{L}}_d, {\widehat{\lambda }}_m$. If $i_{d,MTPA}^{*\prime }$ is not equal to $i_{d,MTPA}^{*}$, $L_{d0}$ in (18) is adjusted online by using the equation shown below which is derived from (23):

$$L_{d0}=\left[\frac{-i_{d,MTPA}^{*}{\widehat{\lambda }}_m}{i_{d,MTPA}^{*}{}^2-{\overline{i}}_{q1}^{}{}^2}+{\widehat{L}}_{q1}\right]+{\beta }_d{\overline{i}}_{d1}$$

(24)

The new value of $L_{d0}$ after adjustment is then substituted into (22), and the RLS algorithm is performed again to estimate the model parameters. The above process is processed continually until $i_{d,MTPA}^{*\prime }=i_{d,MTPA}^{*}$. Moreover, Figure 4 is the flowchart of the proposed estimation algorithm. In order for the proposed estimation algorithm to be better adopted in practical applications, detailed execution steps of the proposed estimation algorithm are described as follows:

(1).

Current injection: Inject d-axis currents and measure $V_{dqi}^{*},i_{dqi},{\omega }_{ei}$, i = 1, 2, 3.

(2).

Finding the lowest stator current: Change d-axis currents to find the lowest stator current and $i_{d,MTPA}^{*}$.

(3).

Smoothing: Use (7) to calculate the smoothing value-based of the measurements ${\overline{V}}_{dqi}^{*},{\overline{i}}_{dqi}, {\overline{\omega }}_{ei}$, i = 1, 2, 3.

(4).

Calculating distorted coefficients and voltage: Calculate current angle and use (8) and (9) to calculate ${\overline{D}}_{di,}{\overline{D}}_{qi}$, i = 1,2,3. Moreover, use (14) to calculate ${\overline{V}}_{deadi}$, i = 1, 2, 3.

(5).

q-axis inductance estimation: Use (15) to estimate ${\widehat{L}}_{qi}$, i = 1, 2, 3.

(6).

Parameters estimation: Use (20) and (22) to estimate ${\beta }_d,{\widehat{\lambda }}_m$, and use (18) to estimate ${\widehat{L}}_{di}$, i = 1, 2, 3.

(7).

Verification: Substitute the estimated parameters into (23) to obtain $i_{d,MTPA}^{*\prime }$ to check if $i_{d,MTPA}^{*\prime }=i_{d,MTPA}^{*}$ or not. If not, go to next step. If yes, then end the algorithm.

(8).

Adjusting: In order to achieve $i_{d,MTPA}^{*\prime }=i_{d,MTPA}^{*}$, use (24) to adjust $L_{d0}$ in (18) and then go back to step 6.

The details of the implementation will be discussed in Section 5.

4. Current-Loop Control Using PID Neural Network Controller

The estimated dq-axis inductances and magnetic flux of the rotor are then adopted in the decoupled control of the current loop as shown in Figure 5, where the PID neural network is represented as PIDNN. Moreover, to improve the control performance and bandwidth of the current loop, an intelligent PID neural network controller proposed in [23] with improved online learning algorithm is adopted to replace the traditional PI controller for the current-loop control. The PID neural network is a three-layered structure. Starting from the two input nodes, it comprises an input layer, a hidden layer, an output layer, and finally an output node, as shown in Figure 6.

Furthermore, the basic function of each layer and the signal propagation of the neural network are introduced as follows:

• Layer 1 (input layer)

The input layer of the PID neural network are designed as:

$${\mathrm{\Phi }}_1(N)=e_{\mathrm{\Phi }}(N)=i_l^{*}(N)-i_l(N)$$

(25)

$${\mathrm{\Phi }}_2(N)={\dot{e}}_{\mathrm{\Phi }}(N)={\dot{i}}_l^{*}(N)-{\dot{i}}_l(N)$$

(26)

where N represents the N th iteration; $l=d, q$.

• Layer 2 (hidden layer)

The input of the hidden layer are the performance measures $u_j(N)$, which can be represented as:

$$u_j(N)={\displaystyle \sum _{i=1}^2{w}_{ij}^1(N){\mathrm{\Phi }}_i(N),j=1, 2, 3}$$

(27)

The outputs of the hidden layer $o_j(N)$ through the respective proportional, integral, and derivative paths can be calculated as follows:

$$o_1(N)=f_P(u_1(N))={\displaystyle \sum _{i=1}^2{w}_{i1}^1(N){\mathrm{\Phi }}_i(N)}$$

(28)

$$o_2(N)=f_I(u_2(N)+o_2(N-1))={\displaystyle \sum _{i=1}^2{w}_{i2}^1(N){\mathrm{\Phi }}_i(N)+o_2(N-1)}$$

(29)

$$o_3(N)=f_D(u_3(N)-u_3(N-1))={\displaystyle \sum _{i=1}^2{w}_{i2}^1(N){\mathrm{\Phi }}_i(N)}-{\displaystyle \sum _{i=1}^2{w}_{i3}^1(N-1){\mathrm{\Phi }}_i}(N-1)$$

(30)

• Layer 3 (output layer)

The output layer can be represented as:

$$y_{\mathrm{\Phi }}(N)={\displaystyle \sum _{j=1}^3{w}_j^2(N)o_j(N)+}{y}_{\mathrm{\Phi }}(N-1)$$

(31)

The first step to design the online learning algorithm of the PID neural network using the supervised gradient decent method is to define an energy function as follows:

$$\mathrm{\Gamma }(N)=\frac{1}{2}{[i_l^{*}(N)-i_l(N)]}^2=\frac{1}{2}{e}_{\mathrm{\Phi }}^2(N)$$

(32)

Then, the learning algorithm is described as follows:

• Layer 3

The error term to be propagated is given by:

$${\delta }_{\mathrm{\Phi }}(N)=-\frac{\partial \mathrm{\Gamma }(N)}{\partial y_{\mathrm{\Phi }}(N)}=-\frac{\partial \mathrm{\Gamma }(N)}{\partial e_{\mathrm{\Phi }}(N)}\frac{\partial e_{\mathrm{\Phi }}(N)}{\partial y_{\mathrm{\Phi }}(N)}=-\frac{\partial \mathrm{\Gamma }(N)}{\partial e_{\mathrm{\Phi }}(N)}\frac{\partial e_{\mathrm{\Phi }}(N)}{\partial \mathrm{\Phi }(N)}\frac{\partial \mathrm{\Phi }(N)}{\partial y_{\mathrm{\Phi }}(N)}$$

(33)

and the connective weight $w_j^2$ is updated by the amount:

$$\mathsf{\Delta }{w}_j^2(N)=-{\eta }_{w^2}\frac{\partial \mathrm{\Gamma }(N)}{\partial w_j^2(N)}=-{\eta }_{w^2}\frac{\partial \mathrm{\Gamma }(N)}{\partial y_{\mathrm{\Phi }}(N)}\frac{\partial y_{\mathrm{\Phi }}(N)}{\partial w_j^2(N)}={\eta }_{w^2}{\delta }_{\mathrm{\Phi }}(N)o_j(N)$$

(34)

where the factor ${\eta }_{w^2}$ is the learning rate for $w_j^2$. The connective weight $w_j^2$ is updated according to the following equation:

$$w_j^2(N+1)=w_j^2(N)+\mathsf{\Delta }{w}_j^2(N)$$

(35)

• Layer 2

By using the chain rule, the connective weight $w_{ij}^1$ is updated by the amount:

$$\mathsf{\Delta }{w}_{ij}^1(N)=-{\eta }_{w^1}\frac{\partial \mathrm{\Gamma }(N)}{\partial w_{ij}^1(N)}=-{\eta }_{w^1}\frac{\partial \mathrm{\Gamma }(N)}{\partial y_{\mathrm{\Phi }}(N)}\frac{\partial y_{\mathrm{\Phi }}(N)}{\partial o_j(N)}\frac{\partial o_j(N)}{\partial u_j(N)}\frac{\partial u_j(N)}{\partial w_{ij}^1(N)}={\eta }_{w^1}{\delta }_{\mathrm{\Phi }}(N)w_j^2{\mathrm{\Phi }}_i(N)$$

(36)

where the factor ${\eta }_{w^1}$ is the learning rate for $w_{ij}^1$. The connective weight $w_{ij}^1$ is updated according to the following equation:

$$w_{ij}^1(N+1)=w_{ij}^1(N)+\mathsf{\Delta }{w}_{ij}^1(N)$$

(37)

Moreover, to reduce the calculation burden of the DSP, the propagation term ${\delta }_{\mathrm{\Phi }}$ can be defined as follows [23]:

$${\delta }_{\mathrm{\Phi }}\cong (i_l^{*}-i_l)+({\dot{i}}_l^{*}-{\dot{i}}_l)=e_{\mathrm{\Phi }}+{\dot{e}}_{\mathrm{\Phi }}$$

(38)

However, (38) will make the $\mathsf{\Delta }{w}_j^2(N)$ shown in (34) always positive. Therefore, the concept of delta learning rule is adopted and (34) is improved and modified as follows:

$$\mathsf{\Delta }{w}_j^2(N)={\eta }_{w^2}{\delta }_{\mathrm{\Phi }}(N)o_j(N)[y_{\mathrm{\Phi }}(N)-y_{\mathrm{\Phi }}(N-1)]$$

(39)

That is to say, the online tuning of $w_j^2$ is according to the derivative of the output of the PID neural network. In addition, the convergence analysis of the adopted PID neural network can be found in the Appendix A.

5. Experimentation

The experimental setup of the IPMSM drive system are shown in Figure 7. The IPMSM test platform is composed of an IPMSM, a gearbox (with gear ratio 4:1), a torque meter and a magnetic powder brake. The detailed information of the magnetic powder brake and IPMSM is listed in

Table 1. Parameters of magnetic powder brake.

Items	Units	Quantities
Torque	Nm	50
Rated current	A	2.15
Coil resistance	Ohm	11.14
Mass of powder	g	60
Maximum rotating speed	rpm	1800

and

Table 2. Parameters of IPMSM.

Items	Units	Quantities
Pole number		8
Rated power	W	2000
Rated line voltage	V	220
Rated current	A	10.6
Rated torque	Nm	9.5
Rated speed	rpm	2000
d-axis inductance	mH	3.48
q-axis inductance	mH	6.16
Magnetic flux	Wb	0.143
Resistance	ohm	0.57
Viscous damping	Nm/(rad/sec)	$2.69\times {10}^{-3}$
Inertia	Nm/(rad/sec2)	$4.07473\times {10}^{-3}$

, respectively. A TMS320F28075 32-bit floating-point digital signal processor (DSP) with 120 MHz is adopted in this study to develop the DSP-based servo drive system. The DSP-based IPMSM drive including a SVPWM CCVSI are also shown in Figure 7. Moreover, a torque meter with 100 Nm/7000 rpm is utilized to measure the load torque. The resolution of the adopted encoder is 2500 pulses/rotation and multiplied by 4 by the DSP. Furthermore, the ratings of the adopted CCVSI is 5 kW/220 V/14 A. The switching frequency 10 kHz is controlled by the SVPWM technology. In addition, the DC link voltage provided by an adjustable DC power supply is set at 311 V. Additionally, the sampling time of the speed and current control loops are 1 ms and 0.1 ms, respectively.

5.1. Online Parameter Estimation Using d-Axis Current Injection

In the experimentation, first, d-axis currents are injected according to Figure 2 and $V_{dqi}^{*}, i_{dqi}, {\omega }_{ei}$ are measured and stored during $T_i$ period of time. Since the pole number of the adopted IPMSM is 8, $T_i$ is 30 ms, 15 ms, 10 ms, and 7.5 ms for 500 rpm, 1000 rpm, 1500 rpm, and 2000 rpm, respectively. Then, the lowest value of the stator current, which could satisfy the MTPA operating point at the specific operating condition, is obtained by varying the d-axis current command gradually. The d-axis current command $i_d^{*}$ is gradually changed from 0 A to −8 A to find out the lowest value of the stator current $I_s$ as shown in Figure 8. The experimental results of the lowest stator current at 500 rpm rotor speed with 4.5 Nm load torque and 2000 rpm rotor speed with rated torque 9.5 Nm are illustrated in Figure 8a,b, respectively. The rotor speed ${\omega }_r$, the q-axis current command $i_q^{*}$, the d-axis current command $i_d^{*}$ and the stator current $I_s$ are all presented in Figure 8a,b. The d-axis current which can lead to the lowest value of the stator current is defined as $i_{d,MTPA}^{*}$, and is −0.86 A in Figure 8a and is −2.6893 A in Figure 8b. The experimental results of $i_{d,MTPA}^{*}$ at various operating conditions are shown in the last row of

Table 3. Estimated ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}, {\widehat{\lambda }}_m$ and $i_{d,MTPA}^{*\prime }$ using initial $L_{d0}$ with $i_{d,MTPA}^{*}$.

	500 rpm 4.75 Nm	500 rpm 9.5 Nm	1000 rpm 4.75 Nm	1000 rpm 9.5 Nm	1500 rpm 4.75 Nm	1500 rpm 9.5 Nm	2000 rpm 4.75 Nm	2000 rpm 9.5 Nm
${\widehat{L}}_{q1}(\mathrm{H})$	0.006065	0.005272	0.006593	0.005528	0.007246	0.005853	0.007618	0.006175
${\widehat{L}}_{d1}(\mathrm{H})$	0.003484	0.003486	0.003479	0.003481	0.003479	0.003478	0.003473	0.003483
${\widehat{\lambda }}_m(\mathrm{W}\mathrm{b})$	0.11625	0.12135	0.11367	0.11507	0.11766	0.11081	0.10969	0.10768
$i_{d,MTPA}^{*\prime }$	−0.9654	−2.3322	−1.2915	−2.8142	−1.4951	−3.2417	−1.6706	−3.5572
$i_{d,MTPA}^{*}$	−0.86	−2.6893	−0.86	−2.6893	−0.86	−2.6893	−0.86	−2.6893

.

According to the flowchart shown in Figure 4, after ${\overline{D}}_{di}, {\overline{D}}_{qi}$ have been calculated using (8) and (9), ${\widehat{V}}_{deadi}$ are calculated by using (14) with the value of stator winding resistance R provided in Table 2. The results are ${\widehat{V}}_{dead1}=4.5807\mathrm{V}$, ${\widehat{V}}_{dead2}=5.02908\mathrm{V}$, ${\widehat{V}}_{dead3}=5.193111\mathrm{V}$ at 4.75 Nm, and ${\widehat{V}}_{dead1}=3.218824\mathrm{V},$ ${\widehat{V}}_{dead2}=3.66749\mathrm{V},$ ${\widehat{V}}_{dead3}=3.888127\mathrm{V}$ at 9.5 Nm. The above results show that the higher the load torque is, the lower the value of ${\widehat{V}}_{deadi}$ is. Moreover, the results are independent of the rotor speed, which can be verified by the results demonstrated in [24]. After ${\widehat{V}}_{deadi}$ has been obtained, ${\widehat{L}}_{qi}$ are estimated by using (15); ${\beta }_d, {\widehat{\lambda }}_m$ are estimated by using (20) and (22); and ${\widehat{L}}_{di}$ are estimated by using (18). Then, $i_{d,MTPA}^{*\prime }$ can be obtained by substituting the estimated parameters into (23). Furthermore, since $\mathsf{\Delta }{i}_{d1}=0$, the unperturbed results ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}$ are regarded as the estimated dq-axis inductances for the decoupled control of current loops. Table 3 shows the resulted ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}, {\widehat{\lambda }}_m$ and $i_{d,MTPA}^{*\prime }$ at various test conditions with different rotor speed and torque load by using the initial value of $L_{d0}$ 3.48 mH. In addition,

Table 4. Required RLS iteration times by using initial $L_{d0}$.

	500 rpm 4.75 Nm	500 rpm 9.5 Nm	1000 rpm 4.75 Nm	1000 rpm 9.5 Nm	1500 rpm 4.75 Nm	1500 rpm 9.5 Nm	2000 rpm 4.75 Nm	2000 rpm 9.5 Nm
Times of 2nd order RLS	1414	1428	438	434	1549	1546	949	948

demonstrates the required RLS iteration times by using the initial value of $L_{d0}$. Since $i_{d,MTPA}^{*\prime }$ at various operating conditions are not equal to $i_{d,MTPA}^{*}$ according to the results shown in Table 3, the estimated ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}, {\widehat{\lambda }}_m$ are not corrected. Therefore, in this study, $L_{d0}$ is modified by using (24). Then, the RLS algorithm is carried out again as shown in Figure 4, and $i_{d,MTPA}^{*\prime }$ is recalculated until $i_{d,MTPA}^{*\prime }=i_{d,MTPA}^{*}$.

Following the above executing process, the resulted ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}, {\widehat{\lambda }}_m$ and $i_{d,MTPA}^{*\prime }$ at various operating conditions with modified value of $L_{d0}$ are shown in

Table 5. Estimated ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}, {\widehat{\lambda }}_m$ and $i_{d,MTPA}^{*\prime }$ using modified $L_{d0}$ with $i_{d,MTPA}^{*}$.

	500 rpm 4.75 Nm	500 rpm 9.5 Nm	1000 rpm 4.75 Nm	1000 rpm 9.5 Nm	1500 rpm 4.75 Nm	1500 rpm 9.5 Nm	2000 rpm 4.75 Nm	2000 rpm 9.5 Nm
${\widehat{L}}_{q1}(\mathrm{H})$	0.006065	0.005272	0.006593	0.005528	0.007246	0.005853	0.007618	0.006175
${\widehat{L}}_{d1}(\mathrm{H})$	0.003776	0.003191	0.004539	0.003578	0.005134	0.003924	0.005557	0.004207
${\widehat{\lambda }}_m(\mathrm{W}\mathrm{b})$	0.11636	0.12122	0.11482	0.11518	0.11263	0.11088	0.11091	0.10805
$i_{d,MTPA}^{*\prime }$	−0.8591	−2.6890	−0.8600	−2.6899	−0.8599	−2.6884	−0.8596	−2.6895
$i_{d,MTPA}^{*}$	−0.86	−2.6893	−0.86	−2.6893	−0.86	−2.6893	−0.86	−2.6893

. Since now $i_{d,MTPA}^{*\prime }$ at various operating conditions are equal to $i_{d,MTPA}^{*}$ according to the results shown in Table 5, the estimated ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}, {\widehat{\lambda }}_m$ can be verified to be correct. Moreover,

Table 6. Required RLS iteration times by using modified value of $L_{d0}$.

	500 rpm 4.75 Nm	500 rpm 9.5 Nm	1000 rpm 4.75 Nm	1000 rpm 9.5 Nm	1500 rpm 4.75 Nm	1500 rpm 9.5 Nm	2000 rpm 4.75 Nm	2000 rpm 9.5 Nm
Times of 2nd order RLS	1549	1431	581	476	1964	1733	1280	1158

is the required RLS iteration times by using the modified value of $L_{d0}$. According to the results shown in Table 5, the values of ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}$ are not the same at different operating conditions, and the higher the rotor speed is, the higher the values of ${\widehat{L}}_{q1}, {\widehat{L}}_{d1}$ are. The same result has also been obtained in [25]. Furthermore, the value of ${\widehat{\lambda }}_m$ is smaller for the operating condition at higher speed with the same load torque [7]. In addition, comparing the results shown in Table 6 with Table 4, the iteration times only increase moderately by using the modified value of $L_{d0}$. After the successful estimation of the motor parameters, the estimated dq-axis inductances and magnetic flux of the rotor are adopted in the following decoupled control of current loops at 1000 rpm with 4.75 Nm and 2000 rpm with 4.75 Nm at two operating conditions.

The DSP-based online parameters estimation and intelligent control for the IPMSM drives are coded in “C” language, compiled into machine codes, and then loaded into TMS320F28075 by using the Texas Instruments Code Composer Studio (CCS). Regarding the coding of the flowchart shown in Figure 4, the contents of Section 2 are coded in the current control loop with 0.1 ms sampling time. Moreover, since the RLS algorithm requires much more computation time, the contents of Section 3 are coded in the speed control loop with 1 ms sampling time. The total operation cycles and execution time for the parameters estimation algorithm shown in Figure 4 at the operating condition of 500 rpm with 4.75 Nm are 572,756,873 cycles and 4.773 s, respectively. In the flowchart shown in Figure 4, changing the d-axis current to find the lowest value of the stator current and $i_{d,MTPA}^{*}$ requires 360,001,438 cycles and 3 s, which is the most time consuming. Furthermore, the RLS iteration time by using the modified value of $L_{d0}$ is 1549, as shown in Table 6, which requires 1.549 s.

5.2. Enhanced Current-Loop Control Using PID Neural Network Controller

The Bode plots measuring scheme of the current loop by using a DSA is shown in Figure 9, where $G_{iv1}=1/(R+s{L}_q)$ is the voltage model of the IPMSM and $G_{c1}$ is the PI or PID neural network current controller. The gains of the PI controller are obtained by trial and error with proportional and integral gains of 5 and 1000, respectively. The sweep sinusoidal wave with resolution 61 µHz is generated from the source of the DSA. The sweep sinusoidal wave, which is also the input of channel 1 (ch1) of the DSA, is regarded as the disturbance $i_{q\_cmd}^{*}$ of $i_q$. Moreover, the difference between $i_q$ and $i_q^{*}$ is adopted as the input of channel 2 (ch2) of the DSA. Analog to digital converter (ADC), serial peripheral interface (SPI) and digital to analog converter (DAC) are implemented as the interface between DSA and DSP. Since the Bode plots measuring scheme of the d-axis current loop is the same as the q-axis current loop, the experimental results are omitted in this study.

In the experimentation, the pre-training process of PID neural network is adopted. Moreover, a PI-type sliding mode control (SMC) [26] is adopted and redesigned as the current controller for the comparison of current control performance. To demonstrate the effectiveness of the proposed current-loop control by using PI, PI-type SMC and PID neural network controllers, various test results are shown in Figure 10, Figure 11, Figure 12 and Figure 13. The measured $i_q^{*}$ and $i_q$ by using PI current controller from no load torque to 4.75 Nm at 1000 rpm are shown in plot a of Figure 10. The measured $i_q^{*}$ and $i_q$ by using PI-type SMC current controller from no load torque to 4.75 Nm at 1000 rpm are shown in plot b of Figure 10. The measured $i_q^{*}$ and $i_q$ by using PID neural network current controller from no load torque to 4.75 Nm at 1000 rpm are shown in plot c of Figure 10. The responses of the online tuning connected weights of the PID neural network controller from no load torque to 4.75 Nm at 1000 rpm can be found in Figure 11. Though good current tracking responses of $i_q$ can be obtained for all PI, PI-type SMC and PID neural network controllers of the inner q-axis current loop, the improvement of the control performance of PID neural network controller is not obvious owing to the control dynamic being dominated by outer speed loop. Furthermore, the measured $i_d^{*}$ and $i_d$ by using PI, PI-type SMC and PID neural network current controllers without MTPA control and with MTPA control at 1000 rpm with 4.75 Nm are shown in plots a, b and c of Figure 12, respectively. The measured $i_d^{*}$ and $i_d$ become negative after the MTPA control being initiated. The responses of the online tuning connected weights of the PID neural network controller can be found in Figure 13. Good current tracking responses of $i_d$ can be obtained for all PI, PI-type SMC and PID neural network current controllers of the inner d-axis current loop. In addition, from the experimental results shown in Figure 11 and Figure 13, the online tuning of the connected weights of the PID neural network controller can guarantee the flexibility and robustness of the neural network control system.

In order to verify the effectiveness and the improved control performance of the PID neural network controller of the inner current loop, the Bode plots measuring scheme of the q-axis current loop by using a DSA, as shown in Figure 9, is employed. The Bode plots of the q-axis current loop using PI, PI-type SMC and PID neural network current controller all at 1000 rpm with 4.75 Nm are shown in Figure 14, Figure 15 and Figure 16. The cutoff frequencies are 283.4 Hz, 393.7 Hz and 410.3 Hz for the PI, PI-type SMC and PID neural network controlled current loops, respectively. Moreover, the Bode plots of q-axis current loop using PI, PI-type SMC, and PID neural network current controller all at 2000 rpm with 4.75 Nm are shown in Figure 17, Figure 18 and Figure 19. The cutoff frequencies are 380.1 Hz, 425 Hz and 431.1 Hz for the PI, PI-type SMC and PID neural network controlled current loops, respectively. From the Bode plots shown in Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19, since the PI-type SMC is a nonlinear controller with high gain, the bandwidth of the current loop is much improved comparing with the PI controller. Furthermore, the proposed PID neural network controller can further improve the bandwidth of the current loop at both test conditions owing to its online tuning and parallel processing capabilities. In addition, all the PI, PI-type SMC and PID neural network current controllers are coded in the current control loop with 0.1 ms sampling time. The operation cycles and execution time of three controllers are 74 cycles/0.6166 μs, 1614 cycles/13.45 μs and 9702 cycles/80.85 μs, respectively. Though the proposed PID neural network current controller is more complicated than both PI and PI-type SMC, the execution time is still within the 0.1 ms sampling time of the current control loop. Besides, choosing the different upper bounds for the lumped uncertainty significantly influences the control performances of the PI-type SMC [26]. Because it is hard to measure the system parameter variations, the exact upper bound value of the lumped uncertainty in the current control loop is always unknown. Although it can be determined by several trials, the constant control gain cannot ensure the robustness of the closed-loop system. The above difficulty can be solved by using the proposed PID neural network current controller due to its uncertainties handling, adaptive and robustness capabilities [23].

6. Conclusions

An online parameter estimation methodology using d-axis current injection, which uses the smoothing values of dq-axis voltages, currents, and electrical rotor speed, was successfully developed and implemented in this study for the estimation of CCVSI distorted voltage and IPMSM parameters in the constant torque region. Moreover, the estimated dq-axis inductances and magnetic flux of the rotor were then adopted in the decoupled control of current loops to ensure the decoupling of the dq-axis in the respective dq-axis current-loop control. Furthermore, an intelligent PID neural network controller was adopted to replace the traditional PI controller to improve the control performance and bandwidth of the current loop. From the experimental results, the distorted voltage term of CCVSI, dq-axis inductances and rotor magnetic flux of the IPMSM have been successfully estimated at various operating conditions. In addition, the bandwidth of the current loop has been effectively improved by using the PID neural network current controller at two test conditions.

The main contributions of this article are listed as follows: (1) An online parameter estimation methodology using d-axis current injection is proposed for the FOC IPMSM drives; a straightforward flowchart is developed to ease the effort of practical implementation. (2) A novel tuning method for the d-axis unsaturated inductance is proposed by using the theory of MTPA with the combination of the RLS method; (3) an intelligent PID neural network current controller is designed to improve the control performance and bandwidth of the current loop.