Enhancing Performance of BLDC: An Improved Fast Terminal Slide Mode Control for BLDC Motor Speed Control

doi:10.21203/rs.3.rs-4802199/v1

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Enhancing Performance of BLDC: An Improved Fast Terminal Slide Mode Control for BLDC Motor Speed Control

https://doi.org/10.21203/rs.3.rs-4802199/v1

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Due to their several merits over brushed DC motors, comprising their superior dynamic characteristics, higher efficiency, a slightly lower noise level, and their utilize of an electronic commutation unit rather than a mechanical one, a brushless direct current (BLDC) motors are in high demand in a wide range of applications. To optimize efficacy and performance, the optimal control method for a BLDC motor operating at different speeds or loads needs to be planned. The objective of this study is for improving the speed control method for BLDC motors operating at various loads or reference speeds. This work suggests an improved method to control the speed of BLDC motors by using the improved fast terminal slide mode control (IFTSMC) technique. With the help of simulation, the suggested strategy's efficiency is evaluated utilizing MATLAB/Simulink software. A comparison is made between the proposed methodology, the proportional integral derivative (PID), and the sliding mode control (SMC) approaches for demonstrating the superiority and robustness of the control method that is offered. In comparison to other methods, the suggested control approach has a lower overshoot value of 0.008%, while 13.1368% for the PID, and 1.3% under the SMC method. Finally, the proposed IFTSMC shows less steady state error (SSE) in the speed responses under all case studies where the SSE of IFTSMC is 0.116745 RPM and this value is better to that of the PID (3.609496 RPM) and SMC (5.316406 RPM).

BLDC motor

slide mode control

terminal slide mode control

speed control

PID

Brushless direct current (BLDC) motor is an abbreviation for a DC electric motor type. This motor lacks brushes, typically used to transfer current to the rotor's windings [1]. On the other hand, a BLDC motor is more efficient and requires less maintenance because external electronics regulate the electrical current that flows through it. Due to their high torque density, small design, and great dependability, BLDC electric motors find extensive application in manufacturing, industry, aerospace, and military sectors [2]. BLDC motors are employed for this purpose because of their benefits over other types of motors [3, 4]. A BLDC motor is smaller, quieter, and more efficient when running since it does not need a commutator-brush section [5, 6]. Since there are no brushes, as the name suggests, commutation is performed electronically using switches to change the current in the windings in response to feedback on the rotor position [7].

A permanent magnet synchronous motor with a trapezoidal back electromotive force (EMF) waveform is the standard definition of a BLDC motor [8]. It allows for accurate control over motor speed, letting for applications with variable or constant speeds [9, 10]. For increasing the motor's lifespan and lessen the chance of damage, the control can also guard against overcurrent, overvoltage, and extremely high or low temperatures. One of the most crucial works in the industrial sector is accurate motion control of the BLDC motors [11, 12]. The optimal BLDC motor drives with speed monitoring can be designed with a suitable speed controller. Deriving an effective controller for servo systems may be challenging because of nonlinear uncertainties and instabilities in the system dynamics in addition to difficult real-world operating circumstances [13].

BLDC motor control is a helpful method for improving abilities and function of the motor [14, 15]. Recently, a number of present control techniques are being put out for the design of BLDC motor speed control. However, in their commercial applications, most BLDC motor control systems still use conventional controllers. This conventional approach has certain disadvantages even though it is simple and easy to use. One of them is that the proportional integral derivative (PID) parameters need to be changed whenever the state of the system changes. This would reduce the device's performance in both static and dynamic modes by causing a delayed reaction and many oscillations. As a result, it is challenging to manage the nonlinearity of BLDC motor characteristics utilizing a traditional PID controller. Fuzzy-PID technique was suggested by scientists in [16] for modeling and building a BLDC motor speed control method. The results of the tests display that the hybridization approach can enhance the motor's performance under different loads.

A reliable control strategy for BLDC motors operated with varying output loads or different input voltage sources was put forth by the authors in [17]. To steady the motor's speed, the field-oriented control (FOC) approach is utilized with slide mode control (SMC). For both the inner and outer loop controllers' sliding surfaces, an exponential reaching law algorithm was suggested. Traction control analysis was done motor performance and applicability. Results showing reduced the oscillation in the electromagnetic motor’s torque and stator currents across a wide range of running speed range were obtained with a cascaded speed and torque controller, which was highly advantageous. In [18] proposed a robust control method for BLDC motor based on improved SMC method. The study was enhanced the dynamic behavior of speed control in BLDC motor by proposing a SMC controller with an enhanced reaching law and integrating sliding surface. The efficacy of the presented controller is evaluated with other current methods, such as conventional SMC, under various test scenarios.

In [19] the authors were proposed a novel hybrid control scheme that uses a fuzzy logic controller in conjunction with a SMC. The goal is to create a strong and quick controller that can overcome the drawbacks of traditional controllers and take use of the quick response of BLDC motors, which are distinguished by their high torque and quick response time. Next, the new controller is introduced together with a proof of its stability. Lastly, a 3 Kw BLDC motor's speed is controlled utilizing the suggested controller approach. The outcomes are contrasted with those of a traditional SMC and fuzzy logic. It makes it possible to demonstrate the suggested controller's rapid response performance. Also, the robust SMC method with reduced chattering phenomena is applied on the BLDC motor in reference [20]. The goal of use this method is for torque operation improvement and smoothing speed control under dynamic load conditions. The authors of [21] described a sensor-less control method for BLDC motor speed regulation that is based on estimating the back EMF. Although there are numerous sensor-less control techniques for BLDC motors, but the suggested method by contrasting it with hall sensor control and the identification of zero crossing points in the back EMF, was proposed good performance. The suggested technique uses terminal voltage and current measurements to estimate rotor location and motor’s speed.

In [22], a neural-network (NN) with PID control method is used and applied on the BLDC motor the goal of this method is to stabilize and smooth the controlling of the speed. Consequently, a NN control based speed control system is developed by looking at the BLDC mathematical model. The MATLAB/Simulink is used to identify the plant model in order to determine the NN block of the BLDC motor drive scheme. The reference control model is meant to supply the ideal control parameter values when the control system responds to the command signal. The suggested method is compared with PID method and the used method show high efficiency, and high time response under different load conditions. In [23], an adaptive neuro-fuzzy inference system (ANFIS) that based on several PID forms as a controller was utilized for regulating the speed of the DC motor. The goal of control is to maintain the rotor speed at the intended reference value even when there are changes in parameters and load torque disturbances. This work has employed a number of PID configurations and ANFIS controllers to regulate the speed of direct current motors. For verifying the superior results of the best controller, the suggested approaches were contrasted with one another. To create training data for the ANFIS, standard configuration, cascade, and dual configuration approaches were applied. The outcomes verified that the ANFIS-based dual PID for DC motor speed control provides outstanding performance, strong resilience, and steady, precise control without oscillation. When compared to other recommended and earlier researched controllers, the controller demonstrated remarkable efficacy and unique performance in evaluating the motor speed tracking performance.

The authors in [24] were presented a new BLDC motor control technique by using nonliners backstepping (BSC) method. The robust controller was adjusted based on gain to track the location of a BLDC motor system. There are two design loops in the controller: an external gain-adaptive loop and an inside, extremely resilient loop. A high efficient control term that is directly synthesized from the speed steady state error is provided to address the issue of internal and external disturbances, while the control unit of the inner loop relies on a BSC method to remove the drawbacks of the system. The Lyapunov-based technique is used for proving the closed-loop system's stability in order for achieving rigorously demonstrated. The suggested hybrid analysis, which combines the ANFIS-based particle swarm optimization (PSO) scheme, can develop the performance analysis of the permanent magnet BLDC (PMBLDC) motor, which was detailed in Ref. [25]. The method known as PSO is created in the presented hybrid control in order for training the ANFIS operation and adjusting the previous and sequent factors. Moreover, the error minimization target function is assessed through the iteration of the PSO method.

The authors in [26, 27] a metaheuristic optimization based control methods are used and applied on BLDC motor drive control. In [26] the improving the effectiveness of BLDC motor control on electric bicycles is the goal of the study. The used study uses computational modeling in the structure of optimizing function formulas and transfer function equations for modeling BLDC motor. The investigation employs the Ziegler-Nichols (ZN) method and firefly algorithm (FA) algorithms as a tuning technique, while the model utilized has the framework of the transfer function. In the present investigation, the FA technique is utilized for determining the ideal values of the PID control parameters ($\:{\text{K}}_{\text{P}}$, $\:{\text{K}}_{\text{I}}$ and $\:{\text{K}}_{\text{D}}$). The outcomes demonstrated that the FA outstand the ZN approach in terms of performance. On the other hand, a grey wolf optimizer (GWO) was suggested to adjust the PID parameters for BLDC motor speed. The proposed GWO algorithm yields superior performance in controlling the BLDC motor speed with high dynamic response and less ripple content in torque compared to particle swarm optimization (PSO) algorithm [27].

This paper's primary goal is to examine three BLDC motor drive control schemes and offer a comparative analysis using both qualitative as well as quantitative evaluations. The explored methods were examined in both steady state and transient operations, among other operating circumstances. BLDC motors are utilized extensively in many different industrial applications owing to their high torque, efficiency, and small size. Thus, BLDC motors are chosen for this purpose due to their advantages over other motor types. Maximum BLDC motor drives employ PID controllers to regulate the machine's speed because they are comparatively inexpensive, have a straightforward design, and function well. However, the primary issue with PID controllers is that they require parameter adjustments to be made throughout implementation. Furthermore, it is difficult to control the nonlinearity of BLDC motor characteristics utilizing a traditional PID controller. So, in this paper, an improved fast terminal slide mode control (IFTSMC) technique for controlling BLDC motor speed is presented. This study discusses a better speed control technique for BLDC motor running at various loads or reference speeds. In general, the IFTSMC control system outperformed the conventional PID and SMC controller in terms of how well the BLDC motor responded. The following is a summary of the study's primary contributions:

A faster convergence speed is achieved compared to conventional control method such as PID and SMC.
High performance of BLDC motor under various values of load torque was attained.
The suggested method presents minimum steady-state error, and a lower overshoot in the BLDC motor’s speed.
The simulation-based MATLAB/Simulink software was used for validating the proposed controller's efficiency.
For showing the originality of the proposed control method, a comparison is done among the suggested IFTSMC, PID, and SMC methods.

The reminder of this article can be divided as: Section 2, presents the methods and materials. The proposed controller is derived in Section 3. Section 4 introduces the results and discussion. Section 5 presents the conclusion of the research.

2.1 Motor modeling

The typical BLDC motor circuit diagram is presented in Fig. 1. As observed in this figure, the overall components of the BLDC motor circuit diagram comprises of three major components: the back EMFs with trapezoidal waveforms, inductance of stator and resistance of stator winding. The BLDC motor is driven through voltage source converter (VSC) and the back EMFs voltages ($\:{e}_{an},\:{e}_{bn},\:$and$\:\:{e}_{cn}$) are displaced 120° from each other in the design of BLDC motor, where the rotor magnetic positions are detected and controlled by electronic commutation method according to the Hall sensors of the stator winding [28, 29]. Each stator winding has the same resistance, and the self and mutual inductances don't change along the course of the winding. The back EMF waveforms of every phase are the same throughout this time. It is feasible to apply mechanical and electrical equations to find the BLDC motor's dynamic equations utilizing the assumption [30]. These formulas are produced using the BLDC motor system's equivalent circuit.

The primary voltage that is applied to the windings is opposed by this voltage. Two hundred and twenty degrees separates the phase angle of each phase's back EMF, which is linked to the rotor position of a three-phase BLDC motor. Finding the precise position of the motor's rotor is necessary for turning on the power devices and initiate the motor by providing the correct commutation sequence. The phase shift with a period of 3600 and an electrical rotation of 120 degrees occurs among each phase current and the back electromagnetic field. To maintain the motor running, this step is required. The procedure that specifies the order for energizing the windings is well-known as "Six Step Commutation" [31].

Figure 1. The general circuit diagram of the BLDC motor powered thru a 3-phase full bridge converter.

The three phase voltage ($\:{v}_{an},\:{v}_{bn},\:$and$\:\:{v}_{cn})\:$equations can be written as follows [32]:

$$\:{v}_{an}={R}_{a}{i}_{a}+\frac{d}{dt}\left({L}_{a}{i}_{a}+{M}_{ab}{i}_{b}+{M}_{ac}{i}_{c}\right)+{e}_{an}$$

$$\:{v}_{bn}={R}_{b}{i}_{b}+\frac{d}{dt}\left({L}_{b}{i}_{b}+{M}_{ba}{i}_{a}+{M}_{bc}{i}_{c}\right)+{e}_{bn}$$

$$\:{v}_{cn}={R}_{c}{i}_{c}+\frac{d}{dt}\left({L}_{c}{i}_{c}+{M}_{ca}{i}_{a}+{M}_{cb}{i}_{b}\right)+{e}_{cn}$$

where $\:{R}_{a}$, $\:{R}_{b}$, and $\:{R}_{c}$ are the phases resistance, $\:{i}_{a}$, $\:{i}_{b}$, and $\:{i}_{c}$ denote the currents of the phases a, b and c, respectively. $\:{L}_{a}$, $\:{L}_{b}$, and $\:{L}_{c}$ represents the self-inductances of the phases, $\:{M}_{ab},\:{M}_{ac},\:{M}_{ba},\:{M}_{bc},\:{M}_{ca},\:\:$and$\:\:{M}_{cb}$ are the mutual inductance between the motor’s phases.

In BLDC motor design, the three phases of it in stator winding are symmetrical, for this reason the self-inductances, resistance, and the mutual inductances are equal. As a result, the following equations (4–6) [32]:

$$\:{R}_{a}={R}_{b}={R}_{c}$$

$$\:{L}_{a}={L}_{b}={L}_{c}=L$$

$$\:{M}_{ab}={M}_{ba}={M}_{ac}={M}_{ca}={M}_{bc}={M}_{cb}=M$$

All of the phase currents added together for a balanced three-phase stator winding are equal to zero at any given time [33].

$$\:{i}_{a}+{i}_{b}+{i}_{c}=0$$

So,

$$\:{M}_{ib}+{M}_{ic}=-{M}_{ia}$$

Using these assumption in phase voltages equations (1–3) and substituting it in Eq. (8), yields the new formulas [34]:

$$\:{v}_{an}={R}_{s}{i}_{a}+\frac{d{i}_{a}}{dt}\left(L-M\right)+{e}_{an}$$

$$\:{v}_{bn}={R}_{s}{i}_{b}+\frac{d{i}_{b}}{dt}\left(L-M\right)+{e}_{bn}$$

$$\:{v}_{cn}={R}_{s}{i}_{c}+\frac{d{i}_{c}}{dt}\left(L-M\right)+{e}_{cn}$$

where $\:L$ shows the self-inductance, $\:M$ presents the mutual inductance and ($\:{L}_{S}=L-M$) denotes the inductance of the equivalent phase. In BLDC motor modelling, the back EMFs with trapezoidal waveforms can be expressed as presented in the below equations [34]:

$$\:{e}_{a}={K}_{e}{\:\omega\:}_{m}{\:f}_{a}\left({\theta\:}_{e}\right)$$

$$\:{e}_{b}={K}_{e}{\:\omega\:}_{m}{\:f}_{b}({\theta\:}_{e}-2\pi\:/3)$$

$$\:{e}_{c}={K}_{e}{\:\omega\:}_{m}{\:f}_{c}({\theta\:}_{e}-4\pi\:/3)$$

where, $\:{K}_{e}$ shows the voltage constant, $\:{\:\omega\:}_{m}$ represents the mechanical speed in rad/s, $\:{\:f}_{a}\left({\theta\:}_{e}\right),{\:f}_{b}\left({\theta\:}_{e}\right),\:\text{a}\text{n}\text{d}\:{\:f}_{c}\left({\theta\:}_{e}\right)\:$are the three-phase trapezoidal wavers [35]. However, the BLDC motor torque (electromagnetic torque) can be written as follows:

$$\:{T}_{em}=\frac{\left({e}_{a}\:{i}_{a}+{e}_{b}\:{i}_{b}+{e}_{c}\:{i}_{c}\right)}{{\:\omega\:}_{m}}\:$$

The electromagnetic torque is formed for driving the mechanical load and under speed acceleration it, the friction and inertia of the motor is overcome. As a result, the real representation of this torque can be expressed as [35, 36]:

$$\:{T}_{em}={T}_{L}+{J}_{m}\frac{d{\:\omega\:}_{m}}{dt}+B{\:\omega\:}_{m}$$

where $\:{J}_{m}$ is the mechanical friction, and $\:B$ is the motor’s inertia.

Figure 2 displays the proposed entire system that implemented in the presented study. As observed, all components of the system details are tabulated in Table 1. For precise speed and position control applications, BLDC motor drives' speed regulation is a crucial component. In this study, the BLDC motor was operated under three speed controller techniques to compare the performance under different conditions. The classical PID method, SMC method and the proposed improved fast terminal slide mode control (IFTSMC). The three phase voltage source inverter (VSI) is applied for driving the BLDC motor via Hall sensors and Control commutation logic scheme. The system is simulated under MATLAB/Simulink software.

Figure 2. The proposed system diagram.

However, a discontinuous controlling technique that takes the time-varying manifold into account is the SMC, which has its roots in the variable structure control theory. Because of its key characteristics, which include stability-based disturbance rejection, robustness, and agility, the SMC is preferred [37]. The SMC architecture features two phases: the reaching phase and the sliding phase. The system's states push in the direction of a predefined sliding surface (s) that corresponds to the starting point on the phase plane during the reaching phase. The simple or the classical slide surface can be written as follows [38]:

$$\:\dot{S}={x}_{1}+{k}_{1}\:{x}_{2}$$

where $\:{k}_{1}>0$ is the constant system. In the proposed BLDC motor system, the state variables of $\:{x}_{1}\:\text{a}\text{n}\text{d}\:{x}_{2}$ can be expressed as:

$$\:\left.\begin{array}{c}{x}_{1}={\:\omega\:}_{m,ref}-{\:\omega\:}_{m}\\\:{x}_{2}=\dot{{x}_{1}}=\dot{{\:\omega\:}_{m,ref}}-\dot{{\:\omega\:}_{m}}\end{array}\right\}$$

where, $\:{\:\omega\:}_{m,ref}$is the reference BLDC motor speed.

It is imperative to enhance the reaching law technique in SMC for multiple reasons such as improving system performance, strengthening resilience, decreasing chattering, and guaranteeing a quicker and more seamless convergence to the sliding surface are the main goals. For this reason, the modified SMC called terminal SMC (TSMC) method was developed. This method can be expressed as follows [39]:

(19)

where $\:{k}_{1}>0\:$is a positive constant and $\:0<\alpha\:<1$. As presented in Eq. (19) the relation between the variables is nonlinear.

However, modifying the TSMC can help reduce or eliminate chattering by providing a smoother control action, thereby preserving system components and improving performance. Accordingly, the fast TSMC (FTSMC) control method is presented in different studies such [40–42]. The slide surface of this method can be written as:

$$\:\dot{S}={x}_{2}+{{k}_{1}\:x}_{1}+{k}_{2}\:{{x}_{1}}^{\alpha\:}\:$$

where $\:{k}_{2}>0\:$is a positive constant. As mentioned in Eq. (20), the FTSMC sliding surface combines the advantages of traditional and TSMC by providing a trade-off between classical SMC and TSMC. Moreover, the exponential equation will become non-real if $\:{x}_{1}$ is negative, hence the issue with negative values is still present.

The stable conditions that achieved by designing the optimal surface is the main goal in the SMC design. Moreover, an optimal control rule should be computed to drive the sliding states towards sliding surface that achieved under searching process with finite time. In the proposed of improved FTSMC (IFTSMC), the surface is designed by presenting a new reaching law as follows:

$$\:\dot{S}={x}_{1}+{{k}_{1}\:x}_{2}+{k}_{2}\:{\left|{x}_{1}\right|}^{\alpha\:}\times\:sign\left(s\right)$$

The time derivate of the surface can expressed as follows:

$$\:\dot{S}={x}_{1}+{{k}_{1}\:x}_{2}+\:f\left(x\right)+g\left(x\right)u+d(x,t)$$

The proposed suggested sliding surface for the BLDC motor case can be written as:

$$\:\dot{S}=\left({\:\omega\:}_{m,ref}-{\:\omega\:}_{m}\right)+{k}_{1}\left(\dot{{\:\omega\:}_{m,ref}}-\dot{{\:\omega\:}_{m}}\right)+{k}_{2}\:{\left|\left({\:\omega\:}_{m,ref}-{\:\omega\:}_{m}\right)\right|}^{\alpha\:}\times\:sign\left(s\right)$$

From equations (21, 22 and 23), the control unit of the system can achieved as:

$$\:u=\frac{1}{g\left(x\right)}\left[-{x}_{1}-{k}_{1}{x}_{2}-\left(f\left(x\right)+D\right)-\:{k}_{2}\:{\left|{x}_{1}\right|}^{\alpha\:}\times\:sign\left(s\right)\:\right]$$

Or the control rule can be written as:

$$\:u=\frac{1}{g\left(x\right)}\left[-\left({\:\omega\:}_{m,ref}-{\:\omega\:}_{m}\right)-{k}_{1}\left(\dot{{\:\omega\:}_{m,ref}}-\dot{{\:\omega\:}_{m}}\right)-\left(f\left(x\right)+D\right)-\:{k}_{2}\:{\left|\left({\:\omega\:}_{m,ref}-{\:\omega\:}_{m}\right)\right|}^{\alpha\:}\times\:sign\left(s\right)\:\right]$$

Moreover, to design the stability analysis of the used sliding surface law, Lyaponov function is provided as:

$$\:V=\frac{1}{2}\:S$$

The conditions of the system stability is proven as follows:

$$\:\underset{s\to\:0}{\text{lim}}\dot{V}=\underset{s\to\:0}{\text{lim}}\dot{SS}\:\le\:0$$

As mentioned above in Eq. (20), the following formula was obtained:

$$\:S\dot{S}=S\left[{x}_{1}+{{k}_{1}\:x}_{2}+\:f\left(x\right)+g\left(x\right)u+d(x,t)\:\right]$$

By substitute the control unit into Eq. (28):

$$\:S\dot{S}=\left[\:\left|S\right|.D-\:{k}_{2}\:{\left|S\right|}^{\alpha\:}\times\:sign\left(s\right).\left|S\right|+d\left(x,t\right).\:S\right]$$

where $\:{\left|S\right|}^{\alpha\:}\ge\:0,\:\:D\ge\:\left|d\right|,\:\text{a}\text{n}\text{d}\:sign\left(s\right)\cong\:\left|S\right|\ge\:0$, all gains in this equation greater than zero. As a result, $\:\dot{V}<0$ and only when $\:S=0$. For this reason, the suggested sliding surface reached the stability conditions.

Table 1

BLDC motor and controllers parameters.
Parameter	Value
Input DC voltage	$\:100\:V$
Reference speed	$\:100-500\:RPM$
Stator resistance	$\:1.43\:{\Omega\:}$
Stator inductance	$\:9.4\:mH$
Rotor flux	$\:0.215\:wb$
Friction coefficient	$\:2{e}^{-3}$
Motor’s inertia	$\:5.5{e}^{-3}\:kg.m²$
Number of poles	$\:4$
$\:{\varvec{k}}_{1}$	$\:0.5$
$\:{\varvec{k}}_{2}$	$\:2000$
$\:\varvec{\alpha\:}$	$\:0.9$

The proposed entire system was modeled and simulated via MATLAB simulation tool. The commutation logic via Hall sensor was utilized for generating the PWM signals of the inverter’s switches. The reference speed and the measured are provided to the three speed controllers to define the optimal control of the speed. For proving the efficiency of the BLDC motor, three different cases are applied on the motor. The motor's ability to manage mild, moderate, and heavy loads is ascertained through testing under various loads, guaranteeing that it can carry out its intended duty efficiently. It is essential to comprehend the motor's response to dynamic variations in load and speed while designing control systems. Moreover, the motor efficiency is verified according to the motor dynamic response. Figure 3 illustrates the suggested system model under Simulink. This model can be describes as follows:

Block (1): describes the reference values of the speed and the load torque that used in the simulation tests.
Block (2): defines the speed control techniques that used in this study which are PID method, SMC method and IFTSMC method. The output of this block is entered the controlled voltage source (CVS) that generate the required DC voltage for the three-phase VSI inverter.
Block (3): defines VSI inverter that used to supply the BLDC motor via six semiconductor MOSFETs and this inverter was powered by the PWM signals via the commutation logic system.
Block (4): defines the model of the BLDC motor. This model contains the chief parameters of the motor such as stator resistor, stator inductance and flux.
Block (5): defines the measuring scopes of the results such as stator currents, back EMFs, speed and torque.
Block (6): defines the hall sensors and commutation logic that generates the required PWM gate signals of the inverter.

4.1. Case Study 1

At this case, the motor reference speed ($\:{\omega\:}_{ref}$) is 265 RPM at interval $\:0\le\:t<6\:s$, and the speed is varied from 265 RPM to 133 RPM for time interval of $\:6\le\:t<11s$. In this case 1 and 2 the load torque or the refernce torque is keep constant of 5 N.m.

$$\:{\omega\:}_{ref}=\left\{\begin{array}{c}265RPM\:,\:0\le\:t<6\:s\\\:133\:RPM\:,\:6\le\:t<11s\end{array}\right.$$

Figure 4 shows the obtained curves for the first case. As observed in this figure, the speed of the rotor is varied from 265 RPM to 133 RPM for the first six seconds. The reference speed value at 6 sec time is drooped to lower value of 133 RPM which makes a small disturbance in the load torque is occurred as displayed in Fig. 4 (b). From this figure, the proposed IFTSMC based control provides fast response and low overshoot in the speed and the electromagnetic torque of the motor. In addition, the measured motor speed is well agreement with its reference speed and the suggested method is very high in terms of convergence time or tracking the reference value.

4.2. Case Study 2

By simulating the BLDC motor under different speed conditions can optimize motor parameters such as dynamic response, and reliability to achieve the best performance under both classical and proposed control methods. For this reason, in second case study, the refernce speed of the motor has the profile as shown in Fig. 5 (a), in this curve the driving cycle proifle is used to represt the real varaitions in the motor speed or torque.

The gathered results for the first scenario are displayed in Fig. 5. The driving cycle profile of the reference speed is used in this test to show the efficiency of the projected control approaches. As observed, the BLDC motor speed is varied from 0 RPM to 167 RPM and then it is raised from zero to 266 RPM. At end of the profile, the maximum speed of this case reaches 442 RPM. According to this figure, the suggested IFTSMC-based control offers the motor's speed and electric torque with quick response times and minimal overshoot. Furthermore, the motor's measured speed agrees well with its reference speed, and the recommended approach has a very quick time of convergence or reference value tracking.

The actual torque of a BLDC motor indeed varies according to the speed reference profile. This relationship is fundamental to understanding the operation and control of BLDC motor based Speed-Torque Characteristics. At lower speeds, the BLDC motor operates in the constant torque region. In this region, the motor can deliver its rated torque up to the base speed. The torque generated by the motor is directly proportional to the current given to it. The motor enters the constant power region when the speed rises above the base speed. In this case, torque reduces inversely with speed to keep output power constant. Usually, field weakening or lowering the effective back EMF is used to accomplish this.

The performance of the BLDC motor under various circumstances of the load torque can be characterized to help with the creation of the proposed efficient control method that can manage both steady-state and transient settings. Under the recommended approach control, the BLDC motor's load torque is managed for modifying the current fed to the motor in order to attain the required speed and torque. This makes it easier to maintain torque in accordance with the speed reference profile.

4.3. Case Study 3

In case 3, the load torque applied on the motor was changed. The constant speed profile with 265 RPM is used. The load torque used in case 3 can be summarized as following:

The reference load at case study 3 is:

$$\:{T}_{ref}=\left\{\begin{array}{c}no\:load\:,\:0\le\:t<6\:s\\\:6\:N.m\:\:,\:6\le\:t<11s\end{array}\right.$$

The dynamic response to change is obtained when there is no load at startup and when there is a transition from no load to full load, as shown in Fig. 6. Based on this finding, the recommended approach more closely complies with the original speed curve when the load changes. When comparing the IFTSMC methodology to the traditional PI and SMC methods, it is evident that there is less chattering. When the motor is converted from the no load to the load (6 N.m), the used IFTSMC control has less overshoot at moment in the actual speed under the disturbance and the suggested method can captures the desired speed value more quickly.

4.4. Case Study 4

The reference load at case study 4 is:

$$\:{T}_{ref}=\left\{\begin{array}{c}12\:N.m,\:0\le\:t<5\:s\\\:6\:N.m\:\:,\:5\le\:t<11s\end{array}\right.$$

When the motor is switched from full load to the half load, the speed is varied as shown in Fig. 7 (a). Also, when there is small load at the end of the operation, the dynamic response to change is realized. Based on this finding, the recommended approach more closely complies with the reference speed curve when the load varies. When comparing the IFTSMC methodology to the traditional PI and SMC methods, it is evident that there is less chattering. The recommended approach can capture the target speed value more rapidly, and the employed IFTSMC control has reduced overshoot at the point in the real speed under the disturbance when the motor is changed from the full load to the load (12 N.m to 6 N.m).

The proposed technique, PID, and SMC approaches are compared in order for proving the innovation of the recommended control method. For comparing and analyze the dynamic performance of control systems, additional comparison is made based on rise time, settling time, steady state error, and overshoot. These metrics provide insights into how a BLDC motor responds to changes, such as load or speed values, which are essential for understanding the system's stability, time of response, and accuracy. For these reason, Fig. 8 was illustrated in this study. As observed in this figure, the raise time of the curves is displayed in Fig. 8 (a), the settling time of the speed results is displayed in Fig. 8 (b), the lower steady state error in the motor’s speed is displayed in Fig. 8 (c), and the overshoot rate in the speed of the motor is demonstrate in Fig. 8 (d). From these figures, the proposed IFTSMC method under all cases has been compared with PID and conventional SMC.

The proposed method shows acceptable raise time especially under case 1 and case 3 (0.0354sec, and 0.0707 sec) when compared with other techniques. In addition, the settling time of the suggested technique for all case is better than obtained under PID or SMC, which makes the used method is more quickly where the best settling time is 0.0434 sec while in PID is 2.2577 sec and for SMC is 0.0661 sec. In this side, the proposed method presents less speed overshoot compared with other methods for case studies especially in case 2.the cases overshoot in the PID are 47.3949%, 13.1368%, 67.3797%, and 67.3797%, respectively. The overshoot in speed curve under classical SMC are 8.7618%, 1.3%, 5.4034%, and 5.4034%. while the best overshoots are obtained in the IFTSMC method which provide 0.01% in case 1, and 0.008% in case 2, 0.7474% for case 3, and the overshot in this method under forth case is 0.7474%. Finally, the lower steady state error (SSE) in the motor’s speed is used to analysis and prove the suggested control method and compare it with other techniques. As observed in Fig. 8 (d) the proposed method indicate lower values of SSE in the speed under all case studies for the system.

The study proposes an improved fast terminal slide mode control (IFTSMC) approach based BLDC motor speed control. Enhancing the BLDC motor's efficiency under various load or reference speed profiles is the aim of this approach. Firstly, the SMC control with different reaching laws are analyzed to clear and derivate the proposed reaching law of the surface sliding and applied it on the motor’s model. Secondly, the BLDC motor is designed and molded by MATLAB/Simulink software to assess its performance and illustrate the efficiency of the utilized technique. From the obtained results, the suggested IFTSMC method is better than the classical control methods based PID and SMC techniques under the same scenarios of the simulation. The BLDC motor is tested with different four cases under varying reference speed and loads. The comparison is added based on rise time, settling time, steady state error (SSE) in addition to overshoot in the motor’s speed. As a result, the proposed control method presents less overshoot value compared with other techniques where the lower overshoot value in IFTSMC is 0.008% and for the PID it is 13.1368%, and it is 1.3% under SMC method.

Author Contribution

I wish to draw the attention of the Editor to the following facts which may be considered as potential conflicts of interest and to significant financial contributions to this work. I confirm that the manuscript has been read and approved by me and that there are no other persons who satisfied the criteria for authorship but are not listed. I confirm that I have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing, I confirm that I have followed the regulations of our institutions concerning intellectual property.

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No competing interests reported.

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Parameter	Value
Input DC voltage	\(\:100\:V\)
Reference speed	\(\:100-500\:RPM\)
Stator resistance	\(\:1.43\:{\Omega\:}\)
Stator inductance	\(\:9.4\:mH\)
Rotor flux	\(\:0.215\:wb\)
Friction coefficient	\(\:2{e}^{-3}\)
Motor’s inertia	\(\:5.5{e}^{-3}\:kg.m²\)
Number of poles	\(\:4\)
\(\:{\varvec{k}}_{1}\)	\(\:0.5\)
\(\:{\varvec{k}}_{2}\)	\(\:2000\)
\(\:\varvec{\alpha\:}\)	\(\:0.9\)

Enhancing Performance of BLDC: An Improved Fast Terminal Slide Mode Control for BLDC Motor Speed Control

Status:

Version 1

Abstract

Figures

1. Introduction

2. Methods and materials

2.1 Motor modeling

3. Proposed Control System

4. Results and Discussion

4.1. Case Study 1

4.2. Case Study 2

4.3. Case Study 3

4.4. Case Study 4

5. Conclusions

Declarations

Author Contribution

References

Additional Declarations

Status:

Version 1