Robustness of Model-Predictive and Passivity-Based Control in the Three-Phase DC/AC Converter Application

Abstract

In modern controller design, various solutions for controlling power converter systems can be found depending on their applications, speed of working, pulse width modulation (PWM) techniques, switching frequencies—$f_c$, and different load types. The need to manipulate control parameters can be often observed in classical structures, e.g., well-known PID, repetitive, or deadbeat control particularly sensitive to distinct parameters uncertainties. The purpose of this paper is to present an improved version of controllers designated for a UPS that will be considerably resistant to model changes. Proposed control techniques are independent of unexpected output filter changes: $L_f$—filter coil inductance and $C_f$—filter capacitor conductance. The second aspect of this paper is to compare effectiveness of modified predictive MPC (model-predictive control) and feedback PBC (passivity-based control) controllers in reducing output voltage total harmonic distortion (THD) for various load values. The biggest distortions of output voltage were observed during experiments with nonlinear RC load. Both simulation and experimental verification of mismatching parameters were performed and examined. Thanks to the proposed solution, the output voltage $TH{D}_v$ quality factor was reduced below 8% in an efficient way for all the applied loads and stayed at the level of 1% when well-matched filter parameters were provided.

1. Introduction

Typical modern feedback or predictive controllers are single-input single-output (SISO) or multiple-input single-output (MISO) controllers [1,2]. In case of the MISO controller in DC/AC converter, an application system analyzes three main input variables [3,4]. Those are output voltage—$v_o$, output current—$i_o$, and filter current—$i_{lf}$. On the other hand, the simplest SISO control method is based only on the output voltage. The main advantage of application of the MISO controller is the effective control functionality and reducing output voltage $TH{D}_v$ [5,6]. Moreover, we should observe a faster outcome of the steady state and lower voltage overshoot for the dynamic load type in comparison with the SISO control mode.

Multiple-input control in the early stage of working is much more effective than other solutions. It provides reduction of different distortions, mainly skewness and unbalancing phenomenon [7]. On the other hand, this type of control is much more burdensome for CPU processing power, which is often limited due to the number of calculations and delays that could occur in an experimental system. That was observed during three-phase Clarke or Park transformation and its reverse transformation for each of the control variables performed simultaneously. It must be also distinguished that the harmonics higher than $f_c$/2 are compensated by the previously implemented $LC$ output filter for the standalone inverter device [7,8].

The designing process of the DC/AC converter should start with designing the $LC$ filter (proper $C_f$ and $L_f$ material selection) and calculating its values [9]. This procedure has a significant influence on the quality of the output voltage $v_o$ [9,10]. Nonetheless, switching frequency $f_c$ value also has a big impact on the control and system stability. Divergence from the previously calculated $LC$ values may occur in the system due to many reasons: electronic component damage or poor quality of manufacturer’s design. However, the designed controller should be able to decrease the values of the output distortion according to the applicable standards, e.g., IEC 61000-2-2, EN 62040-3, and IEEE 519-2014 [11,12,13]. Lower harmonics must be reduced by the feedback control loop or by prediction of the state variables. They are typically implemented in stationary $\alpha \beta$ or $dq$ rotating reference frame in accordance with the three-phase topology and potential necessity of decoupling application.

The motivation behind this paper is to show advantages and disadvantages of the proposed improved controllers dedicated especially for the DC/AC standalone inverters in UPS application [4]. The robustness of the system with an output filter provided with mismatching parameters is highlighted in this study for two forms of MISO control: feedback tracking system with a modulator and state variable prediction without using a modulator. The goal is to discriminate between the two control systems based on two critical performance metrics and recommend the best operation using either passivity or predictive methods.

In this context, especially in terms of controller design, it is preferable to choose a method that allows for a flexible design capable of addressing the issue of having fewer control inputs than control variables while maintaining system stability. Passivity-based control approaches [1,2] provide for a methodical approach to controller design, with the system structure clearly defined. Interconnection and damping assignment (IDA) is one of these strategies. It entails selecting a desirable closed-loop energy function and ensuring that the control error converges to zero. Furthermore, determining controller parameters is, to some extent, easier than in other procedures. For these reasons, IDA-based controllers for various power converters, such as rectifiers and inverters, have already been improved and presented here.

Finite-control-set model-predictive control (FCS-MPC), on the other hand, has become a prominent technique for power converter control [7]. It is built on the premise of employing a discrete VSC model with accompanying filter to forecast future behavior for all potential control inputs, and then applying the one that minimizes a programmed cost function (CF) at each sampling time [9]. This technique has been widely and effectively applied to standalone converters due to its flexibility and intrinsically fast reaction. The online evaluation of all conceivable switch configurations can be performed over many periods, but the number of computations grows exponentially with each step. In this research, an improved algorithm is presented and compared to the enhanced passivity model.

The system design overview for the 2L-VSI will be discussed in Section 2, while the improved passivity-based control will be discussed in Section 3 and the improved model predictive control will be discussed in Section 4. The simulation results and discussion are given in Section 5 and the experimental validations are given in Section 6, while the discussion is reported in Section 7 and conclusions in Section 8.

2. System Design Overview

The three-phase inverter used during investigations is shown in Figure 1. Comparison of the presented solutions is made using both MATLAB simulation and experimental verification. The switching frequency $f_c$ was set to 12.8 kHz—due to utilized hardware components, such as Matlab dSPACE device boards: dSPACE controller, DS5101 and DS2004 A/D, and inverter Danfoss 131F3040, used in empirical tests. The important fact that should be highlighted is that the PBC controller was working with the constant switching frequency and used the $f_c$ as one of its input values in the control law. On the other hand, the MPC algorithm was using an average switching frequency calculated by the cost function J in the currently used operating sector vector depending on the sampling time [14,15]. In the MPC controller, the PWM modulator and the control functions calculations are merged into one state, whereas in the PBC controller the modulator is located at the output of the control function. This fact leads to the assumption that operating frequency was set to 12.8 kHz in order to have a fair comparison between feedback PBC and predictive MPC [16,17]. Typical load types for standalone systems are mainly static-resistive R, dynamic R, and nonlinear rectified $RC$ load. Additionally, the initial values of $L_f$ = 3 mH and $C_f$ = 60 $\mathsf{\mu }$F were taken into calculation during simulation. The paper presents a methodology of designing, implementation, and verification of the two types of MISO controllers—MPC and PBC—with their improved modifications of the control function. Thus, the calculations are based on $\alpha \beta$ transformation. Both of the controllers used the same input variables, output filter values, and were working in the same stress condition—constant input DC voltage—600 V and changeable $L_f$ and $C_f$ values. The installation configuration is presented in Figure 1, and basic parameters of the studied system are listed in

Table 1. Parameters of the studied experimental system.

Parameter	Symbol	Value
DC link voltage	$V_{dc}$	600 V
Switching frequency	$f_c$	12,800 Hz
Nonlinear load (diode rectifier)	$C_L$, $R_L$	460 $\mathsf{\mu }$F, 35 $\mathsf{\Omega }$
Sampling time	$T_s$	39 $\mathsf{\mu }$s
Nominal RMS output voltage (L-L)	$v_{o,ref}$	173 V
Reference wave frequency	$f_{ref}$	50 Hz

.

3. Improved Passivity-Based Control

At the beginning of investigation for that type of control, the object (three-phase inverter) should be described using Euler–Lagrange equations or Port-Hamiltonian energy conversion system analysis [18]. The PCH model ensures interconnection structure related to energy shaping, so it is more beneficial for the PBC controller. In case of passivity control we are focusing on different rules for energy shaping [19,20]. The examined system will be also further referred to as Port-Hamiltonian type. The simplest case of PBC conventional algorithm is based on the linearization of the system equation and its Lagrangian, which is not the purpose of this paper. The IPBC2-used controller is based on IDA-PBC methodology, which consists of the desired interconnections and damping matrices [21]. The next stage is solving the partial differential equation (PDE). The PBC control is the sum of total energy shaping and additionally assumed damping. This type of control is designated for all systems that could store energy on their elements—a typical feedback system that could use energy shaping principle. In the first step, the number of phases should be identified and internal structure of the bridge analyzed—in this case, H type full bridge 2L-VSI. This allows indicating the coefficient of the components in the input matrix. In the next step, based on the equations for each phase, the natural energy must be changed via adding additional resistance $R_i$, named dissipative factor. The controller should track the reference error of the state variable x. The process was first mentioned by Ortega [1]. The system is very often represented in the dq rotationary frame. For investigation, an improvement of the IDA-PBC [22,23] method was investigated—IPBC2 presented in [24], but based on the non-interconnection equations in the matrix J. In that solution, the controlled variables were introduced to the stationary $\alpha \beta$ frame. This is connected to the fact that $\alpha \beta$ leads to obtaining additional derivative factor over the capacitor variable. The only tunable parameters are voltage gain and dissipation factor. That additional tracking affects $K_v$, which is the gain of the output voltage included in the control of each phase. In the calculation it depends on switching frequency, because of the occurrence of the derivatives. This type of control was previously used in other papers, e.g., with the dynamic resistive R load during the unbalanced defects in the delta connected inverter. The system should be described in the $abc$ rotationary frame, taking into account the coefficient depending on the load type, star or delta, and the modulation technique [16,21]. In this study, the star load connection was implemented both for MPC and PBC. The internal matrix coefficients for the Clarke transformation vary in case of the used load type [16]. The load current is treated as an independent disturbance. In case of application of the passivity-based control, the system must fulfill two conditions [1,19]:

• System without the feedback must be stable.
• Stored energy must be lower than supplied energy.

The problem formulation comes down to description of the system by the following Equations (1) and (2). The IPBC2 problem formulations focused on the difference between interconnection matrix and dissipation matrix and handling the error between current and previous states. Based on [21,24], the interconnection does not occur and J is just the identity matrix. $R\left(x\right)$ represents damping matrix, which is the sum of the $R_{Lf}$ and dissipating resistance $R_i$, which is 10. $G\left(x\right)$ represents input matrix, where u is the input vector and $\xi$ is the system disturbance. Input matrix is the DC voltage. During experiments, proper adjustment of the modulation index must be ensured. The system should prevent PWM modulator saturation due to the high-voltage gain response of the output control.

$$\dot{x}=[J\left(x\right)-R\left(x\right)]\frac{\partial H}{\partial x}\left(x\right)+g\left(x\right)u+\xi$$

(1)

The $H\left(x\right)$ represents total stored energy [18,20]; u and y are the input control vector and output voltage, respectively.

$$y=g^{\top }\left(x\right)\frac{\partial H}{\partial x}\left(x\right)+D\left(x\right)u$$

(2)

$$x_{\alpha \beta }=\left[i_{Lf\alpha \beta }{i}_{o\alpha \beta }{v}_{o\alpha \beta }\right]$$

(3)

$$y_{\alpha \beta }=\left[v_{o\alpha }{v}_{o\beta }\right]$$

(4)

The total energy is represented by the Hamiltonian m external port system equation concerning $LC$ circuits [1]. Hence, to the linear system consideration, Hamiltonian has a quadratic form.

$$H\left(x\right)=\frac{1}{2}{x}^{\top }Qx$$

(5)

The state variable could be then rewritten basing on the PH system including necessary interconnection and dissipation matrices $J_{\alpha \beta }$ and $R_{\alpha \beta }$ [1,19].

$$\begin{array}{c}\hfill {\dot{x}}_{\alpha \beta }=[J_{\alpha \beta }+R_{\alpha \beta }]P^{-1}{x}_{\alpha \beta }+G_{\alpha \beta }+D_{\alpha \beta }{d}_{\alpha \beta }\end{array}$$

(6)

$$A_{\alpha \beta }=\left[\begin{array}{ccc}-R_{Lf}/L_f& 0& -1/L_f\\ 0& 0& 0\\ 1/C_f& -1/C_f& 0\end{array}\right]$$

(7)

$$B_{\alpha ,\beta }=\left[\begin{array}{c}1/L_f\\ 0\\ 0\end{array}\right],C_{\alpha ,\beta }=\left[\begin{array}{cccc}0& 0& 1& 0\end{array}\right].$$

(8)

$$R_{\alpha \beta }=\left[\begin{array}{cccc}{R}_i+R_{Lf}& 0& 0& 0\\ 0& R_i+R_{Lf}& 0& 0\\ 0& 0& K_v& 0\\ 0& 0& 0& K_v\end{array}\right]$$

(9)

$$P=\left[\begin{array}{cccc}{L}_f& 0& 0& 0\\ 0& L_f& 0& 0\\ 0& 0& C_f& 0\\ 0& 0& 0& C_f\end{array}\right],J_{\alpha \beta }=\left[\begin{array}{cccc}0& 0& -1& 0\\ 0& 0& 0& -1\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]$$

(10)

$$G_{\alpha \beta }=\left[\begin{array}{cc}{V}_{dc}& 0\\ 0& V_{dc}\\ 0& 0\\ 0& 0\\ 0& 0\end{array}\right],D_{\alpha \beta }=\left[\begin{array}{cc}0& 0\\ 0& 0\\ -1& 0\\ 0& -1\end{array}\right]$$

(11)

$$d_{\alpha \beta }=\left[i_{o\alpha \beta }{i}_{o\alpha \beta }\right]$$

(12)

The total energy in the presented system is the overall sum of the energy stored in the output filters components [24].

$$\begin{array}{c}\hfill G_{\alpha \beta ,dq}=\frac{L_{f}d{i}_{Lf\alpha \beta prev}}{dt}+R_{Lf}{i}_{L\alpha \beta prev}-\\ \hfill -R_i(i_{Lf\alpha \beta }-i_{Lf\alpha \beta prev})+v_{o\alpha prev}\end{array}$$

(13)

For calculation of the IPBC2 controller [24], the value of the reference filter current is needed—$i_{L\alpha \beta prev}$. In this element, it is necessary to take into account the value of the difference between output and reference voltage, so the results should be more robust not only for the output filter current but also for the output filter voltage.

$$K_v\left(v_{o\alpha \beta }-v_{o\alpha \beta prev}\right)$$

(14)

The control law for the stationary $\alpha \beta$ frame for the $K_v=0$ is the same as the one for the conventional PBC [25]. Introducing $K_v$ (the control of the output voltage error) makes the control law IPBC version. The final form consists of the derivative over the output voltage and voltage gain—IPBC2. On the other hand, the derivative over the $C_f$ makes the system stabilize even longer and it is an important factor in the process of decreasing the $TH{D}_v$. During implementation, the system should behave passively. Parameters in

Table 2. Control parameters of the IPBC2 controller, voltage gain—$K_v$, and additional input resistance factor—$R_i$.

Parameter	Value
$K_v$	2
$R_i$	10

maintain stability and passiveness of control. The condition is to store energy less than or equal to the total supplied energy to the system [1]. Additionally, it must be taken into account that passive controllers could modify only destabilizing forces—the forces acting on the system are divided into stabilizing, destabilizing, and supporting ones [1].

4. Improved Model-Predictive Control

Electrical drivers, UPS, and grid-connected inverters have all been proposed as applications for MPC [26,27]. FCS-MPC is based on the principle of employing a discrete model of the power converter and its associated filter to anticipate future behavior for all potential control inputs and then applying the best one that minimizes a predetermined cost function (CF) at each sampling period. The main concept is to harness the microcontroller’s raw processing capability to integrate all control loops in a single algorithm that takes into account the converter’s model and accompanying filter. A three-phase voltage source inverter driven by the FCS-MPC is shown in Figure 1 as a general block diagram.

The method is conducted sequentially in its most basic form, and at the start of each sampling time ($T_s$), it applies new switching configurations generated based on the measurements from the previous step [7]. It then receives new and updated measurements in order to select new switching configurations. The three-phase 2L-VSI power circuit is considered, with the two switches in each leg operating in a complimentary mode [28,29]. The switching states can be represented by the switching signals $S_{ka}$, $S_{kb}$, and $S_{kc}$, which are defined as follows:

$$S_{ka}=\left\{\begin{array}{c}1\mathrm{if}{S}_1\mathrm{on}\mathrm{and}{S}_4\mathrm{off}\\ 0\mathrm{if}{S}_1\mathrm{off}\mathrm{and}{S}_4\mathrm{on}\end{array}\right.$$

(15)

$$S_{kb}=\left\{\begin{array}{c}1\mathrm{if}{S}_2\mathrm{on}\mathrm{and}{S}_5\mathrm{off}\\ 0\mathrm{if}{S}_2\mathrm{off}\mathrm{and}{S}_5\mathrm{on}\end{array}\right.$$

(16)

$$S_{kc}=\left\{\begin{array}{c}1\mathrm{if}{S}_3\mathrm{on}\mathrm{and}{S}_6\mathrm{off}\\ 0\mathrm{if}{S}_3\mathrm{off}\mathrm{and}{S}_6\mathrm{on}\end{array}\right.$$

(17)

The filter inductance ($L_{fa}$, $L_{fb}$, $L_{fc}$) equation can be expressed in the vectorial form as

$$L_f\frac{\mathrm{d}{i}_{L_f}}{\mathrm{d}t}=v_i-v_o$$

(18)

where $L_f$ is the filter inductance and $i_{Lf}$ and $v_o$ are the filter current and voltage, respectively. Variable $v_i$ is the inverter voltage of the system, and it has eight different voltage vectors, as shown in Figure 2.

The equation that describes the dynamic behavior of the output voltage can be expressed as

$$C_f\frac{\mathrm{d}{v}_o}{\mathrm{d}t}=i_{L_f}-i_o$$

(19)

where $C_f$ is the filter capacitance ($C_{fa}$, $C_{fb}$, $C_{fc}$) and $i_o$ is the load current, which can be estimated or measured. These equations can be rewritten in the state space model as [30,31]:

$$\frac{\mathrm{d}X}{\mathrm{d}t}=AX+B_1{v}_i+B_2{i}_o$$

(20)

where,

$$X=\left[\begin{array}{c}{i}_{L_f}\\ v_o\end{array}\right]$$

(21)

$$A=\left[\begin{array}{cc}-R/L_f& -1/L_f\\ 1/C_f& 0\end{array}\right]$$

(22)

$$B_1=\left[\begin{array}{c}1/L_f\\ 0\end{array}\right]$$

(23)

$$B_2=\left[\begin{array}{c}0\\ -1/C_f\end{array}\right]$$

(24)

A discrete model is obtained from (20) and it can be expressed as follows:

$$x\left(\begin{array}{c}k+1\end{array}\right)=A_{q}x\left(\begin{array}{c}k\end{array}\right)+B_q{v}_i\left(\begin{array}{c}k\end{array}\right)+B_{dq}{i}_o\left(\begin{array}{c}k\end{array}\right)$$

(25)

where

$$A_q=ex{p}^{A{T}_s}$$

(26)

$$B_q={\int }_0^{T_s}ex{p}^{A\tau }{B}_{1}d\tau$$

(27)

$$B_{dq}={\int }_0^{T_s}ex{p}^{A\tau }{B}_{2}d\tau .$$

(28)

This model is used to calculate the prediction of filter voltage and currents for every possible input voltage. The selection of the optimal output voltage vector depends on the evaluation of CF. The two different CFs for such system will be [30]:

$$\begin{array}{c}\hfill J={(v_{o\alpha }^{*}-v_{o\alpha }^p(k+1))}^2+{(v_{o\beta }^{*}-v_{o\beta }^p(k+1))}^2+({\lambda }_d\ast g_I)\end{array}$$

(29)

$$\begin{array}{c}\hfill g_I={(i_{Lf\alpha }-i_{o\alpha }+C_f{\omega }_{ref}\left(v_{o\beta }^{*}\right))}^2+{(i_{Lf\beta }-i_{o\beta }+C_f{\omega }_{ref}\left(v_{o\alpha }^{*}\right))}^2\end{array}$$

(30)

where ${\lambda }_d$ = 0.6.

5. Simulation Results

Figure 3, Figure 4, Figure 5 and Figure 6 present the results for the Matlab simulation model output voltages for the nonlinear rectified RC load. The investigations were performed using the load capacitor—$C_L=460$ $\mathsf{\mu }$F to show the controller behavior for the higher load conditions. The value of the output filter capacitor was intentionally increased based on many papers, especially concerning PBC controllers $C_f$ = 60 $\mathsf{\mu }$F [21,22]. During simulations, the overall behavior of the system was examined, including time responses and delays. The figures show the third period due tuning both the controllers. In case of PBC, one period delay was observed in comparison to the MPC output voltage THD stabilization on some constant level. The simulations parameters are based on [24]; however, the system presented in this paper was tuned to the balanced load with changeable filter parameters to maintain the good output voltage quality. The system must fulfill, in the same time, the necessary stabilization conditions for both the controllers. Almost all the results are oscillating about 1% of the output voltage $TH{D}_v$; the most harmful was decreasing the output filter coil.

6. Experimental Validation

The experimental verification assumed downgrading the value of $C_f$, moreover decreasing and increasing the value of the filter inductor. Values used in the presented experiment depended strictly on the manufacturer components. The values of $L_f$ and $C_f$ are presented in

Table 3. $TH{D}_v$ % experimental results for different filter parameters for the nonlinear RC load: $C_L$ = 460 $\mathsf{\mu }$F, $R_L$ = 35 $\mathsf{\Omega }$.

Filter Parameters	MPC Improved %	PBC Improved %
$L_f$ = 3 mH, $C_f$ = 60 $\mathsf{\mu }$F initial	0.97	0.56
$L_f$ = 2 mH, mismatch $L_f$	7.55	4.61
$L_f$ = 4 mH mismatch $L_f$	0.67	1.06
$C_f$ = 40 $\mathsf{\mu }$F mismatch $C_f$	1.09	0.45

. Worse results were obtained for the output filter inductor decreasing. The MPC controller is oscillating on the border of the high-quality S classification according to the EN 62040-3 standard.

In addition, PBC output voltage THD rose to about 5%, the border of the IEEE 519-2014 standard. In Figure 7 and Figure 8, the waveform is a good-quality sine wave, except for the low inductor mismatching case. PBC results in unbalancing between phases and MPC has the problem with the current prediction step to boost the current at the most skew segments of the output voltage. The following observations were made during the experiments (Figure 9). Decreasing values of the inductor filter seemed to considerably deteriorate system behavior. The advantages of increasing capacitor values incurred the risk of the output power factor (PF). Therefore, the capacitor value could not be increased infinitely, even though some power factor correction systems were additionally applied.

7. Discussion

Both simulation and experimental validation of the presented algorithms were performed. Due to the applied algorithms, the total THD harmonic distortion was decreased to the values acceptable in standards, EN 62040-3 for both controllers. MPC- and PBC-improved controllers are good solutions for creating systems that are exposed to changing filter parameters without modifying the internal behavior of the controllers.The used configuration was 2L-VSI and full bridge at input. The main advantage of the used models configuration is the MISO solution. In many papers concerning control techniques for three-phase inverters, single- or double-loop feedback techniques were used but based only on output voltage measurements. The performed investigation proved that models composed of single-input variable are not robust enough; they work efficiently only for an exact model, e.g., deadbeat controller. That leads to a high distortion sensitivity and low-output THD reduction. Response for changes of current must be taken into account. The advantage of the solution is the faster output response. Although the used MPK-made capacitors have very small value of ESR, lack of measuring of the output current and filter current decreases the output voltage harmonic reduction. In this paper, the most efficient configuration was assumed based on [21]. Only two-level regulated VSI provides good output quality with no problem with zero crossing and less dependency on the modulation index. Apart from improved controllers, the $TH{D}_v$ fulfills the standards designated for UPS, even for a mismatched parameters case.

8. Conclusions

In the paper, it was proved that the enhanced MISO version of the classical PBC and MPC are the efficient control techniques for UPS standalone devices exposed for parameter changes. The examined system worked in a robust way in the range of the 12.8 kHz switching frequency. Even though each of the systems use similar input variables control, they are characterized by different abilities. It comes from the fact that MPC uses prediction of the variables’ states and signals, while PBC is based on energy shaping together with the reference measurements. What could be observed during simulations is that the MPC controller kept working with constantly low THD distortion, which was not the case for the PBC. On the other hand, the PBC controller seemed to work slightly quieter due to the constant frequency. Another conclusion is that MPC was characterized by faster time response for at least one period $T_s$, due to lack of the modulator on the input of the device. Additionally, it was shown that both the systems are sensible for downgrading the $L_f$ and $C_f$ filter parameters. Finally both controllers, due to their modification and number of the input tracking variables, are proper solutions when mismatching output $LC$ parameters are provided. They maintain low output distortion $TH{D}_v$, below 8% for all cases and 1% for normal condition. Despite increasing the value of $TH{D}_v$ in case of downgrading the inductor value, the system fulfills requirements for the UPS inverters. Control functions can be directly implemented on a digital microprocessor or using laboratory equipment similar to that presented in the paper. In the future, the investigations could be expanded for the inverters working with different filter types, e.g., LCL, and could focus on the manufacturer’s materials’ parameter values accuracy evaluation.