# Performance analysis of PMSM servo-drive with state feedback and hybrid position controllers

Tomasz Tarczewski, Hubert Lisinski, Lech M Grzesiak

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Tomasz Tarczewski, Hubert Lisinski, Lech M Grzesiak. Performance analysis of PMSM servo-drive with state feedback and hybrid position controllers. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0326. hal-05073862

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Submitted on 19 May 2025

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# Performance analysis of PMSM servo-drive with state feedback and hybrid position controllers

Tomasz Tarczewski<fnref n="1" />,<fnref n="2" />, Hubert Lisinski<fnref n="1" />, and Lech M. Grzesiak<fnref n="2" />

***Index Terms***—Optimal control, Permanent magnet motor, Robustness.

***Abstract***—High-performance operation of servo-drive with permanent magnet synchronous motor (PMSM) is required in many industrial applications, including robotics, machines, and, recently, aircraft components. Complex control structures are necessary to meet the specific requirements of these applications. In this paper, two control structures developed for position control of PMSM servo-drive are presented. The state feedback control (SFC) structure augmented by state variables' limitation and load torque compensation is presented and compared with a hybrid control structure (HSC) where the inner current control loop exists. An experimental evaluation of both control schemes regarding dynamic properties, disturbance compensation, and robustness against the moment of inertia changes is included.

## I. INTRODUCTION

Servo-drives with permanent magnet synchronous motors (PMSMs) are commonly used in motion control applications, e.g., robots and machines [1]–[4]. Reliability, effectiveness, and high torque torque-to-inertia ratio cause these motors to be candidates in new fields of application, such as more electric aircraft (MEA) [5]–[7]. Safety and stability are also required [8].

To achieve precise position control, an advanced control structure is required. Usually, it combines a classical inner control loop with PI-type current controllers operating in *dq* rotating coordinates and a more advanced inner control loop responsible for mechanical variables regulation. In [9], an active disturbance rejection controller (ADRC) is applied in the outer control loop, while the inner one is based on the PI controllers. To obtain optimal coefficients of ADRC, a deep reinforcement learning approach is utilized, and the authors report

higher work efficiency, faster response speed, and better disturbance rejection ability than reference solutions, operating in the cascade manner. In [10], the ADRC scheme is combined with a fractional-order approach to improve the performance of the PMSM servo-drive. It is stated that the proposed strategy outperforms traditional controllers. Since the *q*-axis current is the control signal produced by the proposed scheme, the inner control loop also exists in this solution. An integrated position and speed loop based on sliding-mode control is proposed in [11]. To improve the robustness of the developed approach, the authors propose an optimization of coefficients using the differential evolution algorithm. The inner current control loop supports this control structure as in previous cases.

Contrary to the solutions described above, developing a cascade-free control structure that regulates all necessary servo-drive state variables is possible. In this solution, a cascade control structure does not exist, and therefore, servo-drive behavior should outperform the performance of the cascade one. In [4], an optimal $H_\infty$ controller supported by adaptive extended state observer is proposed. In this solution, the actor neural network provides the optimal control performance, and the experimental results confirm the robustness in case of model perturbations and external disturbances. On the other hand, the authors report the high computation cost and high design complexity. The proposed control scheme is implemented in the dSPACE DS1104, and the PWM inverter carrier frequency is 15 kHz. As shown in [12], an SFC provides a high-performance servo-drive operation and outperforms cascade control structure with PI-type controllers regarding load torque compensation. It also has a relatively low computational complexity, which allows higher switching frequencies ($f_s > 20$ kHz) and implementation in the drive's processor. Due

<footnote n="1">¹ Nicolaus Copernicus University in Torun, Torun, Poland</footnote>

<footnote n="2">² Warsaw University of Technology, Warsaw, Poland</footnote>

<footnote>ttarczewski@umk.pl hubert.lisinski@umk.pl lech.grzesiak@pw.edu.pl</footnote>

<footnote n="1">¹ https://www.int.umk.pl/ ² https://www.isep.pw.edu.pl/</footnote>
to the development of constraint-handling methods, SFC can fulfill MEA requirements, i.e., safety operation and stability [12], [13]. The SFC can be designed as a cascade-free structure where mechanical and electrical variables are simultaneously controlled and as an HSC with an inner current control loop. It seems advisable to check the control performance and the robustness against parameter changes in these two approaches.

In this paper, two position controllers are designed for PMSM servo-drive. Synthesis procedure, control laws formulation, state variables limitation, and load torque compensation are presented. An experimental evaluation of both control structures in terms of dynamic properties, disturbance compensation, and robustness against the moment of inertia changes is included.

## II. MODEL OF PMSM SERVO-DRIVE

A mathematical model of the servo-drive is necessary to design control structures investigated in this paper. The following assumptions precede the modeling process: (i) dynamics and nonlinearities of the voltage source inverter (VSI) have been omitted, (ii) inductances of the motor presented in dq axes are equal (i.e., $L_d = L_q = L_s$), and (iii) a feedback linearization method has been applied to eliminate non-linearities and cross-coupling from the electrical part description. Based on the abovementioned assumptions, the state-space model of the PMSM servo-drive in the dq reference frame has the following form:

$$ \frac{dx(t)}{dt} = Ax(t) + Bu(t) + Ed(t) + Fr(t), \quad (1) $$

with:

$$ x(t) = \begin{bmatrix} i_d(t) \\ i_q(t) \\ \omega(t) \\ \theta(t) \\ e_\theta(t) \end{bmatrix}, \quad u(t) = \begin{bmatrix} u_{ld}(t) \\ u_{lq}(t) \end{bmatrix}, \quad d(t) = T_l(t), $$

$$ r(t) = \theta_{ref}(t), \quad A = \begin{bmatrix} -\frac{R_s}{L_s} & 0 & 0 & 0 & 0 \\ 0 & -\frac{R_s}{L_s} & 0 & 0 & 0 \\ 0 & -\frac{K_t}{J_{nom}} & -\frac{B_m}{J_{nom}} & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{bmatrix}, $$

$$ B = \begin{bmatrix} \frac{K_p}{L_s} & 0 \\ 0 & \frac{K_p}{L_s} \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{bmatrix}, \quad E = \begin{bmatrix} 0 \\ 0 \\ -\frac{1}{J_{nom}} \\ 0 \\ 0 \end{bmatrix}, \quad F = \begin{bmatrix} 0 \\ 0 \\ 0 \\ 0 \\ -1 \end{bmatrix}, $$

where: $i_d(t)$, $i_q(t)$ - current space vector components, $\omega(t)$, $\theta(t)$ - angular velocity and position, $u_{ld}(t)$, $u_{lq}(t)$ - linearized space vector components of voltages, $K_p$ - gain of VSI, $R_s$, $L_s$ - stator resistance and inductance, $B_m$ - viscous friction, $J_{nom}$ - nominal moment of inertia, $K_t$ - torque constant, $\theta_{ref}(t)$ - reference position, $T_l(t)$ - load torque. The last state variable $e_\theta(t)$ introduced in $x(t)$ conforms the integral of angular position error, and it is responsible for the steady-state error-free operation of servo-drive:

$$ e_{\theta}(t) = \int_{0}^{t} [\theta(\tau) - \theta_{ref}(\tau)] d\tau \quad (2) $$

The abovementioned model contains both electrical and mechanical variables of the servo-drive, and therefore, it is suitable to design a state feedback controller.

In the case of HCS, a state-space model should comprise only mechanical variables and $e_\theta(t)$:

$$ \frac{dx_H(t)}{dt} = Ax_Hx_H(t) + B_Hu_H(t) + F_Hr(t) \quad (3) $$

with:

$$ x_H(t) = \begin{bmatrix} \omega(t) \\ \theta(t) \\ e_\theta(t) \end{bmatrix}, \quad A_H = \begin{bmatrix} -\frac{B_m}{J_{nom}} & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}, $$

$$ B_H = \begin{bmatrix} \frac{K_t}{J_m} \\ 0 \\ 0 \end{bmatrix}, \quad F_H = \begin{bmatrix} 0 \\ 0 \\ -1 \end{bmatrix}, \quad u_H(t) = i_{q,ref}(t) $$

In this case, a control signal will be used as a reference value for the current control loop. Linearized differential equations suitable for the synthesis of PI current controllers can be directly derived from the first two rows of (1):

$$ u_{ld}(t)K_p = R_s i_d(t) + L_s \frac{di_d(t)}{dt} \quad (4) $$

$$ u_{lq}(t)K_p = R_s i_q(t) + L_s \frac{di_q(t)}{dt} \quad (5) $$

## III. POSITION CONTROL OF PMSM SERVO-DRIVE

The abovementioned state-space model of the PMSM servo-drive will be used to design position control algorithms. Two cases will be presented in this section: (i) a state feedback control algorithm responsible for controlling mechanical and electrical variables simultaneously, i.e., in a cascade-free manner, and (ii) a hybrid control structure (HCS) with an inner current control loop based on the PI-type controllers and SFC responsible for controlling mechanical variables.
## A. State Feedback Controller

State-space model (1) can be used to design a state feedback position controller. At this stage, a component related to load torque (i.e., Ed(t)) will be omitted. The proposed control law takes the following form:

$$u(t) = -\mathbf{K}_{\text{SFC}}x(t) \quad (6)$$

with:

$$\mathbf{K}_{\text{SFC}} = \begin{bmatrix} k_{x1} & k_{x2} & k_{x3} & k_{x4} & k_{x5} \\ k_{x6} & k_{x7} & k_{x8} & k_{x9} & k_{x10} \end{bmatrix} \quad (7)$$

where: $k_{x1}...k_{x10}$ - coefficients of considered controller. The selection process of (7) has a direct impact on the servo-drive behavior. In this case, the linear quadratic optimization approach was applied to provide optimal coefficients ensuring (i) steady-state error-free for step tracking, (ii) satisfactory dynamics of angular position control, (iii) control strategy with zero d-axis current, and (iv) good load torque compensation.

## B. Hybrid Control Structure

The designing process of a hybrid control structure dedicated to position control of PMSM servo-drive is divided into two main stages. As previously stated, the inner control loop will be based on the PI-type current controllers. The choice is related to the frequent use of this structure [9]–[11]. The control law of PI controller is as follows:

$$\mathbf{u}(t) = K_{pi} \left[ \mathbf{e}_{i}(t) + \frac{1}{T_{ii}} \int_{0}^{t} \mathbf{e}_{i}(\tau) d\tau \right] \quad (8)$$

with:

$$\mathbf{e}_{i}(t) = \begin{bmatrix} i_{d \text{ref}}(t) - i_{d}(t) \\ i_{q \text{ref}}(t) - i_{q}(t) \end{bmatrix},$$

where: $K_{pi}$, $T_{ii}$ - proportional gain and integral time constant of PI controller. In this particular case, the abovementioned coefficients were calculated using an internal model control (IMC) method [14]:

$$K_{pi} = \alpha \frac{L_s}{K_p} \quad (9)$$

$$T_{ii} = \frac{L_s}{R_s} \quad (10)$$

where: $\alpha = \log(9)/\tau_{ri}$, $\tau_{ri}$ - the required rise time of current.

In the second stage, a state feedback controller responsible for the control of mechanical variables is designed. Its synthesis is based on the state-space model (3)

presented in the previous section. The control law takes the following form:

$$u_H(t) = -\mathbf{K}_H \mathbf{x}_H(t) \quad (11)$$

where: $k_{h1}...k_{h3}$ - coefficients of controller. As in the case of SFC described in a previous subsection, the abovementioned coefficients were selected using linear quadratic optimization with the same requirements as in the case of the state feedback controller.

## C. State Variables Limitation

Control law describing the SFC (6) and HCS (11) indicate that both control structures operate in a linear manner and do not take into account the physical constraints of state variables. It is necessary to introduce a constraints handling method to provide high performance (i.e., high dynamics) and safe operation of PMSM servo-drive. In this paper, a model predictive approach constraints (MPAC) has been adopted to imposing constraints on selected state variables. In this concept, discrete predictive formulas based on the state-space model (1) of the servo-drive are utilized to keep selected variables in a desired range. To limit the q-axis current $i_q(n + 1)$ to admissible level, the following formulas derived from the second-row of (1) are used [12]:

$$u_q+(n) = \frac{\text{sat}[i_q+(n+1)]}{\beta K_p} - \frac{\alpha i_q(n)}{\beta K_p} + \frac{e_q(n)}{K_p} \quad (12)$$

$$u_q-(n) = \frac{\text{sat}[i_q-(n+1)]}{\beta K_p} - \frac{\alpha i_q(n)}{\beta K_p} + \frac{e_q(n)}{K_p} \quad (13)$$

where: $u_{q+}(n)$, $u_{q-}(n)$ - the upper and the lower value of q-axis voltage, $\text{sat}[i_{q+}(n+1)]$, $\text{sat}[i_{q-}(n+1)]$ - saturation that ranges the upper and the lower values of the predicted q-axis current between $i_N$, $\alpha = e^{-\tau_i R_s / L_s}$, $\beta = \frac{1}{R_s}(1-\alpha)$, $e_q(n) = p\omega(n)(L_s i_q(n) + \psi_f)$. The third row of (1) is used to calculate $i_{q+}(n+1)$ and $i_{q-}(n+1)$ and to limit the angular velocity of the servo-drive. In the latter task, the following formulas are applied [12]:

$$i_{q+}(n) = \frac{\omega_N}{\delta K_t} - \frac{\gamma\omega(n)}{\delta K_t} + \frac{\hat{T}_l(n)}{K_t} \quad (14)$$

$$i_{q-}(n) = -\frac{\omega_N}{\delta K_t} - \frac{\gamma\omega(n)}{\delta K_t} + \frac{\hat{T}_l(n)}{K_t} \quad (15)$$

where: $\gamma = e^{-\tau_\omega B_m / J_{nom}}$, $\delta = \frac{1}{B_m}(1 - \gamma)$, $\hat{T}_l(n)$ - estimated value of load torque.
<figure><img src="image_2.png" /><figcaption>Fig. 1. Block diagrams of considered control structures with SFC - state feedback controller, LTO - load torque observer, FL - feedback linearization, PI - current controller, SVM - space vector modulator, LPF - low pass filter: (a) SFC, (b) HCS</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Laboratory setup: (a) block diagram, (b) photo of drives and power supplies, (c) electromechanical part</figcaption></figure>

### D. Load Torque Compensation

From the previous subsection, it can be seen that the estimated value of the load torque is applied in MPAC. Its value can also be used to improve the load torque compensation of the servo-drive. In such a case, a control law of SFC (6) should be augmented by the following component [15]:

$$-\mathbf{K}_f d(t) = - \begin{bmatrix} k_{f1} \\ k_{f2} \end{bmatrix} \hat{T}_l(t), \quad (16)$$

with:

$$\begin{bmatrix} k_{f1} \\ k_{f2} \end{bmatrix} = \begin{bmatrix} \mathbf{K}_x & \mathbf{I}_n \end{bmatrix} \mathbf{G}^{-1} \mathbf{E}_x \quad (17)$$

where: $\mathbf{G} = [\mathbf{A}_x \ \mathbf{B}_x]$, $\mathbf{K}_x$ - the first four columns of $\mathbf{K}_{SFC}$, $\mathbf{A}_x$ - the upper-left corner (4x4) of $\mathbf{A}$, $\mathbf{B}_x$ - the

first four rows of $\mathbf{B}$, $\mathbf{E}_x$ - the first four rows of $\mathbf{E}$, and $\mathbf{I}_n$ - the identity matrix of appropriate dimension.

In the case of HCS, the feedforward coefficient $k_f$ is calculated using the same approach as in (17), but the sizes of respective matrices differ: $\mathbf{K}_x$ - the first two rows of $\mathbf{K}_H$, $\mathbf{A}_x$ - the upper-left corner (2x2) of $\mathbf{A}_H$, $\mathbf{B}_x$ - the first two rows of $\mathbf{B}_H$, and $\mathbf{E}_x$ - third and fourth row of $\mathbf{E}$. Block diagrams of the proposed control structures are shown in Fig. 1.

## IV. EXPERIMENTAL RESULTS

### A. Description of the Laboratory Setup

The proposed state feedback control schemes with the constraint handling method were experimentally validated on a prototype PMSM servo-drive. A general
<figure><img src="image_4.png" /><figcaption>Fig. 3. Experimental responses of PMSM servo-drive with $J_{nom}$ and $J_{inc}$ to step changes of angular position: (a) SFC, (b) HCS</figcaption></figure>

block scheme of laboratory setup with two PMSM servo-drives is shown in Fig. 2(a), while a photo is presented in Fig. 2(b). A prototype VSI with SiC power devices supplies a validated PMSM shown in Fig. 2(c), along with additional setup parts. The designed control algorithms with other software components (i.e., SVM, ADCs, QEP, communication) have been implemented in an ARM microcontroller with a Cortex-M4 core from STMicroelectronics. The switching frequency of PWM was set at 22 kHz to provide quiet operation of the drive and to prove the low computational complexity of SFC. The main parameters of the investigated servo-drive are listed in Table I.

## B. Experimental Results

The developed control schemes were investigated in three scenarios, typical for servo-drive applications. To examine the robustness, tests were conducted for the nominal $J_{nom}$ and the increased $J_{inc}$ moment of inertia. The left columns (i.e., (a)) from Figs. 3–5 illustrate the SFC behavior, while the right columns (i.e., (b)) present the HCS maintenance. The quantitative analysis of the servo-drive performance (considering the robustness) is given in the last subsection.

Firstly, PMSM servo-drive was examined for $\theta_{ref} = 0 \to 2\pi \to 0$ rad sequence, and results are presented in Fig. 3. A similar behavior is observed for SFC and HCS

during positioning tasks for nominal moment of inertia. In the case of the increased inertia value, a much higher overshoot is observed for the hybrid control structure. In the case of angular velocity waveforms, one can see a better dynamic performance of the SFC structure than that of HCS. The velocity slope decreases for the increased moment of inertia, and periods with nominal values of q-axis current in transient are longer. This proves the proper operation of the constraint-handling method. Regardless of the moment of inertia value and control structure, the d-axis current is maintained at zero.

<table><caption>TABLE I
SELECTED PARAMETERS OF SERVO-DRIVE</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value & Unit</th></tr></thead><tbody><tr><td>Rated angular velocity</td><td>ω<sub>N</sub></td><td>50 rad/s</td></tr><tr><td>Rated current</td><td>i<sub>N</sub></td><td>5 A</td></tr><tr><td>Stator resistance</td><td>R<sub>s</sub></td><td>1.05 Ω</td></tr><tr><td>Stator inductance</td><td>L<sub>s</sub></td><td>12.68 mH</td></tr><tr><td>Nominal moment of inertia</td><td>J<sub>nom</sub></td><td>8.6 · 10<sup>-3</sup> kgm<sup>2</sup></td></tr><tr><td>Increased moment of inertia</td><td>J<sub>inc</sub></td><td>17.7 · 10<sup>-3</sup> kgm<sup>2</sup></td></tr><tr><td>Viscous friction</td><td>B<sub>m</sub></td><td>1.4 · 10<sup>-2</sup> Nms/rad</td></tr><tr><td>Torque constant</td><td>K<sub>t</sub></td><td>1.14 Nm/A</td></tr><tr><td>Switching frequency</td><td>f<sub>s</sub></td><td>22 kHz</td></tr><tr><td>DC-link voltage</td><td>U<sub>dc</sub></td><td>200 V</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Experimental responses of PMSM servo-drive with $J_{nom}$ and $J_{inc}$ to step changes of angular position: (a) SFC, (b) HCS</figcaption></figure>

In the second test, the sequence $\theta_{ref} = 0 \rightarrow 4\pi \rightarrow 0$ rad was applied, and results are presented in Fig. 4. Similar behavior is observed for both analyzed control structures for a nominal moment of inertia, as in the previous case. A higher reference position value causes periods with nominal values of angular velocity and q-axis current in transient to be longer. This proves the proper operation of the MPAC for the servo drive's mechanical and electrical variables, also for increased moment of inertia. In the case of the increased inertia value, a longer transient is observed for the hybrid control structure.

Finally, the ability for load torque compensation has been investigated, and results are shown in Fig. 5. It can be seen that a much better load torque compensation is observed for the SFC structure compared to the hybrid one with $\tau_{ri} = 500 \ \mu s$ in the current control loop. It is worth noting that the steady-state value of the q-axis current during load torque compensation $t \in (1, 2 \ \text{s})$ is lower for SFC.

### C. Performance analysis

As was previously shown, the proposed control schemes have been investigated for nominal and increased moment of inertia. Firstly, the performance of

both structures was analyzed using the ISE performance index:

$$ISE(t) = \int_{0}^{t_f} [\theta_{ref}(\tau) - \theta(\tau)]^2 d\tau \quad (18)$$

where $t_f$ – the integration time. Values the rise time ($t_r$) and the ISE are calculated for experimental responses shown in Fig. 3, namely for the first step of the reference position, i.e., for $t \in (0, 0.8) \ \text{s}$. These are summarized in Table II.

<table><caption>TABLE II
PERFORMANCE INDICATORS FOR $\theta_{ref}$ STEP CHANGE</caption><thead><tr><th rowspan="2"></th><th colspan="2">SFC</th><th colspan="2">HCS</th></tr><tr><th>$J_{nom}$</th><th>$J_{inc}$</th><th>$J_{nom}$</th><th>$J_{inc}$</th></tr></thead><tbody><tr><th>$t_r$ [ms]</th><td>125</td><td>163</td><td>147</td><td>162</td></tr><tr><th>ISE</th><td>3.5</td><td>5.1</td><td>3.8</td><td>5.3</td></tr></tbody></table>

It can be seen that the rise time for nominal moment of inertia is significantly lower for SFC, resulting lower ISE value. In the case of increased moment of inertia, $t_r$ and ISE increase and are similar for both considered control structures.

The maximum value of the angular position error caused by the load torque variations ($\delta_{\theta}$), the recovery
<figure><img src="image_6.png" /><figcaption>Fig. 5. Experimental responses of PMSM servo-drive with $J_{nom}$ and $J_{inc}$ to step changes of load torque: (a) SFC, (b) HCS</figcaption></figure>

time ($t_{rec}$) observed after imposing the load torque are computed for results presented in Fig. 5, i.e., for $t \in (0, 2)$ s. The same time period was used to calculate the *ISE* performance index. The abovementioned values are summarized in Table III.

<table><caption>TABLE III
PERFORMANCE INDICATORS FOR $T_l$ STEP CHANGE</caption><thead><tr><th rowspan="2"></th><th colspan="2">SFC</th><th colspan="2">HCS</th></tr><tr><th>$J_{nom}$</th><th>$J_{inc}$</th><th>$J_{nom}$</th><th>$J_{inc}$</th></tr></thead><tbody><tr><td>$\delta\theta$[rad]</td><td>0.011</td><td>0.01</td><td>0.11</td><td>0.09</td></tr><tr><td>$t_{rec}$[ms]</td><td>642</td><td>705</td><td>821</td><td>1500</td></tr><tr><td>$ISE$</td><td>9.9 &middot; 10<sup>-6</sup></td><td>1.1 &middot; 10<sup>-5</sup></td><td>2.5 &middot; 10<sup>-3</sup></td><td>5.6 &middot; 10<sup>-3</sup></td></tr></tbody></table>

Based on Table III, it can be concluded that a much better load torque compensation is observed for the SFC structure. Due to the lack of the inner control loop, rapid generation of the electromagnetic torque is possible, resulting in a much lower position perturbation in all considered cases.

Finally, the sensitivity formula based on the *ISE* performance index was applied to examine the robustness of developed control systems against the moment of inertia variations [16]:

$$S_{ISE}^{J_m} = \frac{dISE}{dJ_m} \frac{J_{nom}}{ISE_{nom}} \quad (19)$$

where: $dISE = ISE_{inc} - ISE_{nom}$ – fluctuation of the performance index, $dJ_m = J_{inc} - J_{nom}$ – fluctuation of the moment of inertia. Based on (19), it can be concluded that the more sensitivity function approaches zero, the less *ISE* performance index is influenced by the moment of inertia variations. For $S_{ISE}^{J_m} = 1$, variation of the moment of inertia directly corresponds to an equal variation of *ISE*. The sensitivities calculated for the step changes of the reference position $S_{ISE}^{J_m}|_{\theta_{ref}}$ and for the step changes of the load torque $S_{ISE}^{J_m}|_{T_l}$ are listed in Table IV.

<table><caption>TABLE IV
SENSITIVITY VALUES</caption><thead><tr><th></th><th>SFC</th><th>HCS</th></tr></thead><tbody><tr><td>$S_{ISE}^{J_m}|_{\theta_{ref}}$</td><td>0.41</td><td>0.37</td></tr><tr><td>$S_{ISE}^{J_m}|_{T_l}$</td><td>0.06</td><td>1.16</td></tr></tbody></table>

From these results, it can be seen that a similar value of sensitivity is observed for a step change of the reference signal. Such a behavior can be explained by the same control structure (SFC) responsible for regulating mechanical variables in both analyzed control schemes. In the case of the load torque step change, the performance SFC outperforms the HCS. These prove that
a cascade-free state feedback controller ensures superior load torque compensation and robustness against mechanical parameter variations and can be recommended for MEA applications.

## V. CONCLUSION

In this paper, selected control algorithms were implemented and experimentally verified in PMSM servo-drive. It was found that the state feedback position controller provides similar dynamical properties and superior load torque compensation compared to the hybrid control structure. A lack of the cascade control structure with the inner control loop responsible for current regulation in HCS causes it.

Because of the similarity of mechanical variables control structures (i.e., SFC), the robustness observed for the reference path is similar in both cases. The robustness analyzed for the disturbance path is much better for SFC. It is also proven that the MPAC is immune against the moment of inertia changes. Therefore, SFC with MPAC can be recommended for high-performance applications where superior load torque compensation is required.

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