Servo Motor Control Matlab

Servo Motor Speed Control

Ngoc Son Vu1*, Van Cuong Pham1,2, Phuc Anh Nguyen1,

My Linh Dao Thi2, Thanh Hai Vu2

Abstract: This research proposes a Sliding Mode PID (SMC-PID) controller to improve the speed control performance of DC servo motors, which are widely used in industrial applications such as robotics and CNC. The objective of the proposed controller is to enhance the speed control performance of DC servo motors on the CE110 Servo Trainer. The proposed method integrates a traditional PID controller with a sliding mode control mechanism to effectively handle system uncertainties and disturbances. Experimental results show that the SMC-PID method provides significant improvements in accuracy and stability compared to traditional PID controllers, with metrics such as reduced overshoot, shorter settling time, and increased adaptability to system uncertainties. This research highlights the effectiveness of the SMC-PID controller, enhancing the performance of DC servo motor speed control.

Figure: System Model & Simulation Flow for Servo Motor Control Matlab

Keywords: Sliding Mode PID controller, Robust control, DC Motor, CE110 Servo Trainer.

1. Introduction

DC servo motors play a vital role in modern industrial systems, including robots, CNC machines, and precision drives. Their high accuracy and fast response make speed control a key research focus. However, practical applications often face challenges such as disturbances, parameter variations, and system uncertainties, which degrade control performance .

Figure: System Model & Simulation Flow for Servo Motor Control Matlab

Among the various control methods currently applied, the PID control strategy has been maintained as a fundamental approach due to its simple structure, ease of implementation, and satisfactory performance in a wide range of applications.

Despite its widespread use, certain limitations have been identified in conventional PID controllers, particularly when systems operate under uncertain conditions or are subjected to external disturbances . To address these limitations, several

494

advanced control strategies have been investigated and applied, including fuzzy logic control, sliding mode control (SMC), backstepping control, and other intelligent algorithms. Fuzzy logic control has been utilized to handle system nonlinearities and uncertainties effectively, particularly in robotic manipulator applications . Sliding mode control has been recognized for its robustness against disturbances and model uncertainties in nonlinear dynamic systems .

Additionally, adaptive backstepping control techniques have been developed to enhance trajectory tracking performance in complex robotic systems under parameter variations and external disturbances .

In this study, a control scheme integrating the classical Proportional-Integral- Derivative (PID) controller with Sliding Mode Control (SMC), referred to as SMC- PID, has been proposed to enhance the speed regulation of DC servo motors implemented on the CE110 Servo Trainer platform. The approach has been formulated by embedding a sliding mode control law into the conventional PID framework in order to improve robustness and adaptability in the presence of system uncertainties and external disturbances . The performance of the proposed controller has been experimentally validated and compared with that of the traditional PID controller. Improvements have been observed in terms of tracking accuracy, transient response, and overall system stability .

The research is structured as follows: ection 2 introduces the CE110 Servo Trainer and its MATLAB/Simulink model. Section 3 details the PID-SMC controller design. Section 4 presents experimental results comparing SMC-PID with conventional PID. Section 5 concludes and suggests future research directions.

2. System Description

The experimental setup employs the CE110 Servo Control System by TecQuipment , comprising a DC motor, linear load, speed measurement unit, and an electrically controlled variable load, as depicted in Figure 1.

Figure 1. Block diagram of the feedback control system – CE110 Servo Trainer

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In this system, 𝑉 denotes the input voltage applied to the motor, 𝜔 epresents the angular velocity of the motor shaft, and 𝜃 refers to the angular position of the shaft.

The output signals 𝑦ఠ and 𝑦ఏ correspond to feedback signals from the speed and position sensors, respectively . The CE110 by TecQuipment, interfaced with a computer via the PCIe-6321 control board, ensures efficient communication and control. Motor speed is regulated by the input voltage, with an encoder measuring and transmitting transient speed data for analysis. The experimental setup includes a CE110 Servo Trainer, PCIe-6321 board, and a PC with MATLAB/Simulink.

Calibrated At 1V Per 200 Rpm For

precise control and monitoring.

3. Pid-Smc Controller Design

To enhance performance and robustness, a hybrid PID-SMC controller is proposed, combining the steady-state accuracy of PID with the robustness of SMC. The control signal 𝑢(𝑡) consists of two main components:

ௗ௧ Is The Conventional Pid

control term. And 𝑢ௌெ஼(𝑡) = −𝜂. 𝑠𝑖𝑔𝑛(𝑠(𝑡)) is the sliding mode control term designed to ensure robustness against uncertainties and external disturbances. Here, 𝑒(𝑡) = 𝜔௥௘௙(𝑡) −𝜔(𝑡) is the speed error, and 𝜔௥௘௙(𝑡) is the desired speed trajectory. The sliding surface is defined as:

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Where: 𝜆ଵ, 𝜆ଶ are positive constants selected to shape the convergence dynamics of the error. To reduce chattering from the discontinuous sign function in practical scenarios, a saturation function or boundary layer approach is applied:

(3)

To ensure system stability under the proposed PID-SMC controller, the

𝑢(𝑡) = 𝑢௉ூ஽(𝑡) + 𝑢ௌெ஼(𝑡)

Assume the closed-loop system dynamics are of the form:

Substituting 𝑢(𝑡) Into 𝑠̇(𝑡), We Have:

𝑠̇(𝑡) = 𝜆ଵ𝑒̇(𝑡) + 𝜆ଶቂ𝑓(𝑒, 𝑒̇) + 𝑏. ൬𝑢௉ூ஽(𝑡) −𝜂. 𝑠𝑎𝑡ቀ

(8)

Group all bounded terms (including PID and nonlinear dynamics) into a

∅ቁቚ≤1 Then 𝑉̇(𝑡) ≤−𝜀|𝑠(𝑡)| < 0 For Some 𝜀> 0

Thus, 𝑉̇(𝑡) < 0 proving that the closed-loop system is globally asymptotically stable in the Lyapunov and the tracking error converges to zero.

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

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Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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