farhan a. salem · farhan a. salem . abstract —this paper proposes a new generalized and refined...

International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 555 ISSN 2229-5518

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New refined Model for Mechatronics design of solar mobile robotic platforms

Farhan A. Salem Abstract—This paper proposes a new generalized and refined model for Mechatronics design of Solar Electric Mobile Robotic Platforms (SEMRP) and some considerations regarding design, modeling and control solutions. The proposed models are developed to help in facing main challenges in developing Mechatronics mobile robotic systems, in particular; early identifying system level problems and ensuring that all design requirements are met, and developed to allow designer to 0Thave the maximum output data to to select, 0Tdesign, tested and analyze overall SEMRP system and each subsystem outputs characteristics and response, for desired overall and/or either subsystem's specific outputs, under various PV subsystem input operating conditions, to meet particular SEMRP system requirements and performance. The proposed SEMRP system model consists of five main subsystems, each subsystem is mathematically described and corresponding Simulink sub-model is developed, then an integrated model of all subsystems is developed, tested and evaluated0T for desired system requirements and performance, t0The obtained results show the simplicity, accuracy and applicability of the presented models in Mechatronics design of SEMRP system applications, as well as, for application in educational process. Index Terms—Mechatronics, Solar Electric Mobile Robotic Platform (SEMRP), PV Panel, Modeling/simulation.

—————————— —————————— 1. INTRODUCTION 5T The 2T5Tessential characteristic 2T5T and 2T5Tthe key2T5T to success in 2T5TMechatronics2T5T design is a 2T5Tbalance between2T5T two sets of skills5T modeling/analysis and experimentation / hardware implementation skills. Modeling, simulation, analysis and evaluation processes in Mechatronics design consists of two levels, sub-systems models and whole system model with various sub-system models interacting similar to real situation, the subsystems models and the whole system model, are tested and analyzed 0Tfor desired system requirements and performance [1]. Mobile robot is a platform with a large mobility within its environment (air, land, underwater) it is not fixed to one physical location. Mobile robots have potential application in industrial and domestic applications. Generally, Mobile robots are a relatively new research area that is not normally considered from several different perspectives. Different researches on Mobile robots fundamentals, mathematical and Simulation models can be found including but not limited to in [1-222T]2T, most of it study separate specific system or subsystem design, dynamics analysis, control or application. Solar electric mobile platform (SEMRP) system is relatively new field of mobile robots and new research area, a generalized refined model of overall SEMRP system that can represent the actual system dynamics and that can be used in Mechatronics mobile robotic system design is of concern.

------------------------------------------------------------------ Farhan A. Salem

P P

is currently with Taif University Saudi Arabia. Dept. of Mechanical Engineering, Mechatronics engineering

6T

prog.6T

, College of Engineering, and Alpha center for Engineering Studies and Technology Researches, Amman, Jordan. Email: [email protected] One of the simplest and most used structures in mobile robotics applications, are the two-wheel differential drive mobile robots shown in Fig. 1, it consists of a chassis with

two fixed and in-lines with each other electric motors and usually have one or two additional third (or forth) rear wheel(s) as the third fulcrum, in case of one additional rear wheel, this wheel can rotate freely in all directions, because it has a very little influence over the robot’s kinematics, its effect can be neglected [12]. Accurate designing and control of mobile robot is not a simple task in that operation of a mobile robot is essentially time-variant, where the operation parameters of mobile robot, environment and the road conditions are always varying, therefore, the mobile robot as whole including controller should be designed to make the system robust and adaptive, improving the system on both dynamic and steady state performances. To help in facing the two top challenges in developing Mechatronics systems; early identifying system level problems to optimize system level performance to meet the design requirements and ensuring that all design requirements are met, as well as, while maintaining desired accuracy, to simplify and accelerate Mechatronics design process of mobile robots, including proper selection, analysis, integration and verification of the overall system and sub-systems performance throughout the development process, this paper extends writer's previous works [15-16] [23-27] and proposes new generalized and refined model for Mechatronics design of SEMRP system, the proposed model is to be developed to allows designer to 0Thave the maximum output data to select,0T integrate, tested and analyze the SEMRP system for desired overall and/or either subsystem's outputs under various PV system operating conditions, to meet particular SEMRP system requirements. The proposed SEMRP system and its block diagram representation are shown in Fig. 1(a)(b), the SEMRP system consists of five main subsystems including; PV panel, DC/DC converter, mobile platform, actuator, control unit , each subsystem, to be mathematically described and corresponding Simulink sub-model developed , then an integrated design of all subsystem is to be developed, the subsystems models and the whole SEMRP system model, are to be tested and analyzed 0Tfor desired system requirements and performance0T

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Fig. 1(a) The block diagram of proposed SEMRP system configurations and control

Fig. 1(b) The block diagram of proposed SEMRP system configurations and control

DC motor

Rig

ht w

heel

Gears

Mob

ile P

latf

orm

Tach

o

Electronic components; Controller , drive, Power supply

Lef

t w

heel

Solar panel

Tach

o

Fig. 1(c) Solar electric mobile robotic platform (SEMRP)

system 2. SEMRP system modeling The proposed SEMRP system and block diagram representation is shown in Fig. 1(a)(b), it consists of five main subsystems including; PV panel, DC/DC converter, mobile platform, DC machine and control unit subsystems, each subsystem, each subsystem is to be mathematically described and corresponding Simulink sub-model developed, then an integrated generalized design of overall SEMRP system of integrated subsystems will be developed, to result in generalized SEMRP system, the subsystems models and the whole SEMRP system model, are to be

tested and analyzed 0Tfor desired system requirements and performance0T. 2.1 Modeling of mobile platform A detailed description, fundamentals, mathematical and Simulink models of mobile robots can be found in different resources, most of it study separate specific system or subsystem design, dynamics analysis or control, including [1-222T]2T. In [14] Proposes a new refined mathematical, Simulink and function block models for mobile robots and some considerations regarding Mechatronics design and control solutions are proposed and tested. In [15] Mechatronics design of electric machine and corresponding motion control in terms of desired output position or velocity, for desired deadbeat response specifications are proposed and tested, the proposed design can be used for different Mechatronics motion control design application where the proper selection of actuating machine and design of precise motion control system are of concern, the design can be simplified, accelerated and evaluated, using both or either of proposed new MATLAB built-in function named deadbeat( ). In [16] mathematical and Simulink models of mobile robot in the form of wheeled chair are proposed and

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controlled to achieve desired output performance and speed. In [18] dynamic analysis and control of mobile robots using a proposed generalized model are proposed. In [19] Design and implementation of an experimental mobile robotic system is proposed, a model of designed robot was created in environment of the ADAMS simulation software and the electrical drive system was modeled in the Simulink software, the obtained data was used in the process of determination of appropriate driving motor, moreover, the real experiments with constructed robot were accomplished in order to verify the performed simulations. In [20] proposed models that be used for simulation and control of mobile platforms, the proposed models take into account the hardware limitations, friction force and the topography of the environment for out door navigation. In [21] Introduced modeling of power components and computer simulation as a tool for conducting transient and control studies of mobile robots. In [22] some considerations regarding mathematical models and control solutions for two-wheel differential drive mobile robots, where the closed loop control diagrams for position control and respectively for direction control in tracking along imposed trajectories are developed, analyzed and included. 2.1.1 Actuator subsystem modeling In order to drive a SEMRP, induction motors, reluctance and permanent magnet motors can be used, the actuating machines most used in Mechatronics motion control applications are PMDC machines (motors).In this paper, PMDC motor is considered as SEMRP electric actuator, based on this, the SEMRP system motion control can be simplified to a PMDC machine motion control. depending on application requirements, any other actuating machine can also be used to replace PMDC motor to develop a generalized model. Considering that the DC motor subsystem dynamics and disturbance torques depend on mobile platform shape and dimensions, in modeling DC motors and in order to obtain a linear model, the hysteresis and the voltage drop across the motor brushes is neglected, other DC motors types can be used, where the input voltage, VRinR maybe applied to the field or armature terminals [28]. A detailed mathematical description and Simulink models of DC machine has been studied for last decades, and can be found in different resources including; [12-17][26-27][29].

In [16-17] a detailed derivation of DC machine and mobile robotic platform mathematical and Simulink models are derived and developed, as well as, function block with its function block parameters window, based on these references, the DC motor system dynamics are expressed as given by Eq.(1),The coulomb friction can be found at steady state, to be as by Eq.(2).Since the open loop transfer function of SEMRP system is simplified to DC motor open loop transfer function, the equivalent SEMRP system open loop transfer function with load and gears attached, in terms input voltage, VRinR(s), and shaft output angular velocity, ω(s), is given by Eq.(3).The geometry of the mechanical part determines the moment of inertia, the SEMRP system can be considered to be of is cylindrical shape , with the inertia calculated as given by Eq.(4) , where the total equivalent inertia, JRequiv Rand total equivalent damping, bRequiv Rat the armature of the motor with gears attaches, are given by Eq.(5). The inertias of the gears and wheels have to be included in the calculations of total equivalent inertia, as by Eq.(5) KRtR iRa R = TRαR + TRω R+ TRload +RTRfR

(1)

KRtR iRa R - b*ω = TRf R

(2)R

2

( )( )

( )/

( ) ( ) ( )

platformspeed

in

t

a equiv a equiv equiv a a equiv t b

sG s

V sK n

L J s R J b L s R b K K

ω= =

= + + + +

R

R(3)

2 2

1 1

2 2

232 1

2

( )12

equiv m Load equiv m Load

load equiv motor gear wheel

N Nb b b J J JN N

NbhJ J J J J mrN

= + ⇔ = +

= ⇔ = + + +

R R(4)R

R R In the following calculation the disturbance torque, T, is all torques including coulomb friction, and given by (T=TRloadR+TRfR), and correspondingly, the open-loop transfer function of the PMDC is given by Eq.(5). Based on Eq. (3), two Simulink models of DC machine subsystem shown in Fig. 2(a)(b) are developed , these sub-models will be used in

this paper to represent DC machine sub-model..

( ) ( )( )2

( )( )

( )/

( )

platformopen

in

t

a a equiv equiv a a b t

sG s

V sK n

L s R J s b s L s R T K K

ω= =

=+ + + + +

(5)

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angular speedCurrent,i

Torque

EMF constant Kb

Torque

l inear acceleration

linear speed.

Angular Speed

Kt

torqueconstant

-K-

rad2mpsV=W*r1

1/n

gear ratio, n

1

La.s+Ra

Transfer function1/(Ls+R)

1

den(s)

Transfer function1/(Js+b).

Torque

Step,V=12,

Kb

Inclination angle

Angular speed

Load torque

Load torque sub-system

Inclination

Inclination angle

du/dt

Current.

Mobile_robot4.mat

Mobile_robot3.mat

Mobile_robot2.maMobile_robot1.mat Mobile_robot.mat

.

Fig. 2(a) DC machine sub-model in Simulink

current ,id/dt

anglul. speedAngul. speed

Torque

Current

Motor Torque

linear speed.

sum

-K-rad2mpsV=W*r2

anlge

Vin=12

Torque.

Motor3.mat

To File3

Motor2.mat

Motor1.mat

Motor.mat

Inclination angle

Angular speed

Load torque

Load torque sub-system

-K-Kt

Kb

Kb

1s

1s

Integrator

1/Jm

Inertia , 1/Jm

Inclination

Inclination angle

[mobile_W]

bm

Damping, b

Current

Angular speed

Ra

Ra

1/La

1/La

[mobile_W]

Ang. speed

Fig. 2(b) DC machine sub-model in Simulink

Fig. 2(a)(b) open loop Simulink model of DC machine subsystem sub-model with load torque

2.1.2 Modeling of SEMRP platform dynamics. In [14] is introduced a detailed derivation of refined mobile platform mathematical and Simulink models including most possible acting forces, tested and verified. Several forces are acting on mobile platform when it is running, the modeling of a mobile platform system dynamics involves the balance among the acting on a running platform forces, and these acting forces are categorized into road-load and tractive force. The road-load force consists of the gravitational force, rolling resistance of the wheels, the aerodynamic drag force and the aerodynamics lift force. The resultant force is the sum of all these acting forces, will produce a counteractive torque to

the driving motor, i.e., the tractive force. The disturbance torque to mobile platform is the total resultant torque generated by the acting forces, and given by Eq.(6).The driving force comes from the powertrain shaft torque, which can be written as the wheel torque, given by Eq.(7), This wheel torque provides the resultant driving, tractive force, FT to the platform, and referring to Fig. 3, the relationship between the resultant tractive force and the torque produced by the motor Ts ,can be obtained as shown in Eq.(8) .The platform inertia torque can be defined by Eq.(9). It is required to couple the mobile platform with the wheel rotational velocity via characteristics of the electric motor and surface such as the traction force, the torque, etc. The relationship between the linear velocity of the platform,

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v, and the angular velocity of the electric motor is given by Eq.(10):

(6) a Lin_a ang_aF F F FTotal R CF F= + + + +

wheel shaftT n Tη= (7)

, wheel shaftTotal shaft Total

T n T rF T Fr r n

ηη

= = ⇒ = (8)

vehiclVehicl

dT J

dtω

= (9)

*wheelrn

ωυ = (10)

To determine the electric battery capacity, and correspondingly design of the Photovoltaic panel with series and parallel connected cells, it is required to estimated energy required by platform, the required power in kW that platform must develop at stabilized speed can be determined by multiplying the total force with the velocity of the SMEV, and given by Eq.(11):

( ) * *Total TotalP F Fυ υ= ∑ = (11) R Electrical power (in watts) in a DC circuit can be calculated by multiplying current in Amps and V is voltage, and given by Eq.(12).Based on fundamental principle of dynamics the acceleration of the vehicle is given by Eq.(12): P= I x V (12)

*m totalP PM

αυ

−= (13)

The driving force comes from the powertrain shaft torque, which can be written as the wheel torque, given by Eq.(7). This wheel torque provides the resultant driving, tractive force, FRTotalR to the vehicle and given by Eq.(14):

* *wheel shaftTotal

wheel wheel

T n TFr r

η= = (14)

Referring to Fig. 3, the relationship between the resultant tractive force and the torque produced by the motor TRshaftR ,can be obtained as by Eq.(15):

**

wheelshaft Total

rT Fn η

= (15)

The platform inertia torque can, also, be defined by relationship given by Eq.(16):

platformplatform

dT J

dtω

= (16)

When modeling mobile platform, considering desired accuracy and platform system dimensions, the following most acting forces and corresponding torques, can be considered: The rolling resistance force,

rolling _ r rF C C cos( )normal forceF Mg α= = (17)

For motion on a level surface, α=0, cos(α)=1 , and Eq.(17) becomes:

rolling _ r rF C Cnormal forceF Mg= = (18)

In terms of the vehicle linear speed Eq.(17) becomes: ( )rolling r0 r1F M g C -C * ( )signυ υ= (19)

The rolling resistance coefficient CRrR ,is calculated by expression given by Eq.(20):

r3.6C 0.01 1100 robotυ = +

(20)

The rolling resistance torque is given by Eq.(21) ( )rolling rT C cos( ) wheelMg rα= (21)

The hill-climbing resistance force is given by Eq.(22): ( )climb slopeF F = sin( )Mg α= (22)

The hill-climbing resistance, slope, torque, is given by Eq.(23):

( )climb slopeT T = sin( ) wheelMg rα= (23)

The total inertia force of the mobile platform , is given by Eq.(24),The inertia torque is given by Eq.(25):

inertia slopedF F Mdtν

= = (24)

( )2 inertia sl wheelopedT T M rdtν = =

(25)

The Aerodynamic Drag force, given by Eq.(26),Considering car and wind speed Eq.(26) become:

2aerod dF 0.5 AC vehiclρ υ= (26)

( )2aerod dF 0.5 AC ( )vehicle wind vehiclesignρ υ υ υ= +

( ) ( )2aerod dF 0.5 AC vehicl wind vehicl windsignρ υ υ υ υ= + +

The aerodynamics torque is given by Eq.(27).The aerodynamic drag coefficient CRdR : characterizing the shape of the SMEV and can be calculated using expression, given by Eq.(28):

2aerod d

1T AC2 vehicle wheelrρ υ =

(27)

aerod2

F0.5DC

Sρυ= (28)

The aerodynamics lift force, FRliftR; given by Eq.(29).The coefficient of lift CRLR, with values ( CRLR to be 0.10 or 0.16), can be calculated using expression given by Eq.(30):

20.5lift L vehicleF C Bρ υ= (29)

20.5LLC

Aρυ= (30)

The force of wind , FRwindR ; can be calculated by Eq.(31):

( )2wind dF 0.5 AC vehicle windρ υ υ= + (31)

The angular acceleration force , is the force required by the wheels to make angular acceleration and is given by Eq.(32):

2

acc_ angle 2Fwheel

GJ ar

= (32)

The angular acceleration torque is given by Eq.(33):

(33) 2 2

acc_ angle 2 wheelwheel wheel

G GT J a r J ar r

= =

The linear acceleration force FRaccR : is the force required to increase the speed of the SMEV and can be described as a linear motion given by Eq.(34):

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acc 2F * wheelJd dM a M Mdt dtrυ υ = = = +

(34)

accF *TdM a M M

dt Jω

= = = ∑

Substituting derived equations in total force equation, we have, expression given by Eq.(35):

[ ] ( )

( ) ( )r0 r1

2d Linear_acc

2

sin( ) M g C -C * ( )

0.5 AC F

Total

vehicl wind vehicl wind

wheel

F Mg sign

sign

J dMr dt

α υ υ

ρ υ υ υ υ

υ

= + + + + + + +

(35)

α

M*g

Road incl.

r =ν/ω

Solar panel

sun

Fig. 3 Forces acting on moving solar electric mobile robotic

platform. Considering shape of mobile platform as cylinderical , the aerodynamic drag coefficient is found from aerodynamic force as follows,: the drag force is found by FRaR= τRmR * A , where : τRmR :shear stress and found by equation ( )m 0 du / dy |yτ µ == . Where: μ: air dynamic

viscosity 1.5x10P

-5P . A: frontal area of platform

(A=0.58*0.92=0.5336mP

2P). ν: The linear speed of the mobile

platform (0.5 m/s), substituting and calculating we find Aerodynamic drag coefficient CRd R=0.80,CRd Ris not an absolute constant for a given body shape, it varies with the speed of airflow (or more generally with Reynolds number RReR. νRoR : The speed of the wind (m/s), against the direction of the platform's motion, r: wheel radius 0.075 m. ρ: The air density (kg/mP

3P) at STP, ρ =1.25, At 20°C and 101 kPa, ρ

=1.2041,

The air density is calculated by below expression, where: ρRoR = 101325 Pa, sea level standard atmospheric pressure, TR0R = 288.15 K sea level standard temperature. G = 9.81 m/sP

2P.

Earth-surface gravitational acceleration. L = 0.0065 K/m temperature lapse rate. R = 8.31447 J/(mol*K) universal gas constant. M = 0.0289644 kg/mol molar mass of dry air.

**

0** 1

*

g mR L

oO

L hMT

R T

ρρ

−

=

Load torque modeling and simulation; In [14], based on application and platform size, a detailed derivations of different models of mobile robotic platform and corresponding Simulink models, are developed. Based on derived equation the maximum calculated load torques, for the mobile robot to overcome, is simulated in Simulink refined load-torque sub-model and mask shown in generalized model shown in Fig.7 , based on desired accuracy and application other representations can be developed including shown in Fig. 4(a)(b)(c)(d), where three versions of load torque are proposed, first model of acting forces and corresponding torques shown Fig. 4(a) and second simplified model for mobile platform of medium size applications shown Fig. 4(b), in this model, the following forces can be included; the hill-climbing resistance force FRclimb,R aerodynamic Drag force , FRaerodR and the linear acceleration force FRaccR, and to be given by Eq.(36). The load torque can be further simplified to include the total inertia force of the mobile platform, the total weight component of the robot, and the total friction force between the wheels and the topography’s surface with the viscous rolling friction coefficient the corresponding Simulink sub-models is shown in Fig. 4(c). The input to load-torque sub-model is shaft angular speed ω, the motor torque KRtR*IRa R for coulomb friction calculations and changes in the road surface, inclination angle, α as a disturbance introduced to the system.

20.5 sin( )DdF AC Mg mdtυρ υ α= + + (36)

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The hil l-climbing slope, torqueM*g*sin(a)*r

The inertia torque

Coloum Friction

1 Load torque

r^2*m/2

m*g*Cr*r

The roll ing resistance torque M*g* Cr*cos(a)*r

(0.50*ru*reference_area*r)

The aerodynamics lift force = 0.5*ru*B*CL*v^2

(0.50*rou*front_area*Cd)*r

The aerodynamics drag torque 0.5*ru*A*Cd*V^2*r

sin(u)cos(u)

SinCos.

du/dt

Derivative,-K-.

.

m*g*r

3Kt*Ia

2

Inclination angle

1Angular speed

Fig. 4(a) load torque refined Simulink model

1Load Torque

r

0.5*rou*front_area*Cd

mr*m*g

Terminator

sin(u)cos(u)

SinCos

du/dt

Derivative

2 Angular speed1 Inclination angle

Fig. 4(b) load torque of medium size and accuracy platform model

Rolling friction coefficient

1Load Torque

1

zeta

m*r^2r*m*g

Terminator

sin(u)cos(u)

SinCos

du/dt

Derivative

2 Angular speed1 Inclination angle

Fig. 4(c) The simplified load torque of platform model

inclination angle

Load Torqueangular speed

Angular speed

Inclination angle

Load torque

Load torque subsystem

Inclination

inclination angle

Load Torque

angular speed

Inclination angle

Kt*Ia

Angular speed

Load torque


Inclination

Fig. 4(d) Simulink model load torque mask

2.2 Sensor subsystem modeling

Tachometer is a sensor used to measure the actual output angular speed, ωRLR. Dynamics of tachometer can be represented using Eq.(37), assuming the SEMRP system, is to move with linear velocity of 0.5 m/s, the angular speed is obtained as shown by Eq.(38). Therefore, the tachometer

constant, for calculated angular speed ω, is given as shown by Eq.(38), any other desired platform output speed can be choosing based on this approach, for example for output linear speed of 0.5m/s , ω =0.5/0.075=6.667 and KRtach R =12/6.667=1.8

( ) ( ) ( ) ( )( )

outout tach out tach tach

d t V sV t K V t K K

dt sθ

ωω

= ⇒ = ⇒ = (37)

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1 12 13.3333rad / s 0.9r 0.075 13.3333

tachKνω = = = ⇒ = = (38)

2.3 Generalized Photovoltaic Panel –Converter (PVPC) subsystem model The PV panel is used as electricity generator to convert the irradiance from sunlight into electricity using photovoltaic system to generate its own power for propulsion and for storing in batteries, and use power converter as a device that converts electrical energy source with variable needs of the electric vehicle by switching devices .The PV Panel-Converter (PVPC) system consists of two main subsystems; PV panel and DC/DC buck converter with battery subsystems. The PVPC system consists of two main subsystems; PV panel and DC/DC converter with battery subsystems, each subsystem will be separately, mathematically modeled and simulated in MATLAB/Simulink, and then an integrated generalized and refined model that returns the maximum output data, for design and analysis, will be developed and tested. The generalized mathematical and Simulink Photovoltaic Panel –Converter (PVPC) subsystem model and sub-models, considered in this paper are d in reference to [24-25]. 2.3.1 Photovoltaic cell-Panel subsystem modeling A general mathematical description of a PV cell in terms of output voltage, current, power and of I-V and P-V characteristics has been studied for over the past four decades and can be found in different resources, many of which are listed in [24]. The output net current of PV cell I, and the V-I characteristic equation of a PV cell are given by Eq.(39), it is the difference of three currents; the light-generated photocurrent IRph R, diode current IRd Rand the shunt

current IRRSH R. The output voltage, current and power of PV array vary as functions of solar irradiation level β, temperature T , cell voltage V and load current I, where with increase in temperature at constant irradiation, the power output reduces, also, by increasing operating temperature, the current output increases and the voltage output reduces, similarly with irradiation. Therefore the effects of these three quantities must be considered in the design of PV arrays so that any change in temperature and solar irradiation levels should not adversely affect the PV array output to the load/utility [24]

( )( )

( )

( )

I

I I I 1

I

I 11000

S

S

d RSH

q V IRSNKT

ph ssh

q V IR

ph

SNKTsc i ref s

sh

I

V R IeR

V R I

I I

I K T T eR

β

+

+

= − −

+= − − −

+

= + − − − −

(39)

The generalized mathematical and Simulink models of PV cell, considered in this paper are built in reference to [25-26], the modified model and mask are shown in Fig. 5(a)(b), as shown, this generalized PV cell- array model is designed 0Tto allow designer to have maximum 0Tnumerical visual and graphical data 0T to select, design 0Tand analyze a given PV system for desired output performance and characteristics under given operation condition, including; cell's-panels current, voltage, powers, efficiency and fill factor. Running model given in Fig. 5(d), for PV parameters defined in Table 1, at standard operating conditions of irradiation β=1000, and T=25, will result in P-V and I-V characteristics shown in Fig. 5(c)(d) and shown visual numerical values of cell's-panels current, voltage, powers, efficiency and fill factor, these curves show that, this is 3.926 Watt PV cell with IRSCR = 8.13 A , Vo= 0.6120V , IRmaxR =7.852 A , VRmaxR =0.5 V, (MPP = IRmaxR * VRmaxR =7.852 *0.5=3.926).

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Is

Iph

Id

Ish

I

VP

V

V

I

P

cell current

5Cell power

4 Cell I out

3Cell Vout

2 Panel I out

1Panel Vout

Nm

cell/model1

V1

I.mat

To File2

P.mat

To File1

V.mat

To File

24

PV module output voltage

0.5

PV cell voltage

Module V

Cell P-V

Cell I-V

BB0

1000

.8

.7

.6

.5

.4

.3

.2

.1

K

.'

PV.mat

.

,.

eu

,

eu

,

''6

''4

''3

''2

''1

''

N

'

Ns

series cells

23

1

Vo

.

Rs

Ki

Rsh

Tref

1

1

Isc

q

1.438

3V

2B 1

T

I

Fig. 5 (a) PV cell (module) Simulink subsystem model [25].

Cell surface area

P

V

Nm

Parallel cells

Panel current

Panel voltage

0.1445

1.438

0.7188

0.5

1.438

0.5

43.13

24

T

B

V

A

Ns

Np

Panel V out

Panel I out

Cell Vout

Cell I out

Power in

Power out

Cell Ef f iciency

Fill Factor

PV Panel Subsystem

Cell voltage

Cell power out

Cell power in

Cell efficiency

Cell current

Cell P-V

Cell I-V

V

.

''3

Ns

Series cells

B

sun Irrad

T

A

Fig. 5 (d) Generalized PV Cell(module) Simulink model [25]

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Fig. 5 (c) V-I Characteristics for β=1000, and

T=25 Fig. 5 (d) P-V Characteristics for β=1000, and

T=25

2.3.2 DC/DC Converter subsystem modeling Power converters can be classified intro three main types; step-up, step-down and step up and down. Most used and simple to model and simulate DC/DC converter include 9TBoost,9T Buck and buck-boost9T converter 1T9Ts. 1T[24-25]. In this paper step-down DC/DC Buck 9T converter 1T9Ts1T is used. In [24], different models of Buck converter are derived, developed in Simulink and tested, including Buck converter circuit diagram shown in Fig. 6(a) and Simulink sub-model and masks shown in Fig. 6 (b)(c), also In [24] generalized Photovoltaic panel-Converter (PVPC) system Simulink model, shown in Fig. 6(d), is developed by integration both PV panel and converters subsystems sub-models resulting in model shown in Fig. 6(e). These Fig. show the outputs of both PVPC subsystems when tested for defined parameters listed in Table-1 including duty cycle of D=0.5. Duty cycle is the ratio of output voltage to input voltage is given by Eq.(40):

*out oninout in

in out on off

V TID V D V DV I T T

= = ⇒ = ⇔ =+

(40)

Where: IRoutR and IRinR, : the output and input currents. D : the duty ratio (cycle) and defined as the ratio of the ON time of the switch to the total switching period. In this paper, the PWM generator is assumed as ideal gain system, the duty cycle of the PWM output will be multiplied with gain Kv= KRDR, This equation shows that the output voltage of buck converter is lower than the input voltage; hence, the duty cycle is always less than 1. 2.3.3 Generalized Photovoltaic Panel–Converter (PVPC) subsystem model Based on presented Simulink two sub-models of SEMRP system, PV panel subsystem and DC/DC converter subsystem , a generalized system model of PVPC system can be proposed and in generalize SEMRP system model shown in Fig. 6 (d)(e)

Vpv PWM

Vout

Vin

converter Vout

Duty cy cle, D

Vin

Vc

IL

Vo

Subsystem

KD

PWM gain

Vin

24

.

'1'

Converter output power

Vc

converter output current Iout

11.99

24

17.25

11.99

11.99

1.439

Fig. 3(a) Buck converter circuit diagram[24] Fig. 3 (b) Buck converter Simulink model, based on refined math

model[24]

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3Vo

2IL

1Vc

Product

Duty cy cle, D switchin signal (0,1) PWM

PWM Generator Subsystem

R/(L*(R+Rc))

1/(C*(R+Rc))

1/L

12.02

R/(R+Rc)

1s

((RL+Ron)+((R*Rc)/(R+Rc)))/L

(R*Rc)/(R+Rc)

R/(C*(R+Rc))

1s

2Vin1

Duty cycle, D

Fig. 6 (c) Buck converter subsystems model [24]

Pout

13PV panel Power out

12Fill Factor

11PV cell efficiency

10PV cell Power out

9PV cell Power in

8 PV cell current out

7PV cell Volt out

6PV panel current out

5PV panel Volt out

4Converter Power out

3Volatges comparision

2Converter voltage out

1Converter current out

Terminator

Product



T

B

V

A

Ns

Np

Panel V out

Panel I out

Cell Vout

Cell I out

Cell Power in

Cell Power out

Cell Ef f iciency

Fill Factor

PV Panel Subsystem1

Duty cy cle, D

Vin

Vc

IL

Vo

Buck converter Subsystem

''1

7Np

6Ns

5Cell surface

area A

4V

3Irradiation, B

2T

1Duty cycle

Fig. 6 (e) Generalized PVPC system sub-models consisting of three subsystems; PV panel, converter and PWM sub-

models

Cell power

[Cell_Vout]

[Cell_Iout]

Cell P-V

Cell I-V

,.

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Vout

Vin

PV_con8.mat

PV_con7.mat

PV_con6.mat

PV_con5.mat

PV_con4.mat

PV_con.mat

PV_con3.mat

PV_con2.mat

PV_con12.mat

PV_con10.mat

PV_con9.mat

PV_con1.mat

Step D

Duty cy cle

T

Irradiation, B

V

Cell surf ace area A

Ns

Np

Conv erter current out

Conv erter v oltage out

Volatges comparision

Conv erter Power out

PV panel Volt out

PV panel current out

PV cell Volt out

PV cell current out

PV cell Power in

PV cell Power out

PV cell ef f iciency

Fill Factor

PV panel Power out

PV-Converter Subsystem

PV panel power in

PV cell output volt

PV cell output current

PV cell efficiency

[Cell_Vout]

[panel_Vout]

Nm

Ns

A

V

.

B

sun Irrad

11.99

24

System Vin-Vout comparision

Converter current Iout

1.439

D

Duty cycle, D

Converter Volt Iout

1.438

0.5

43.13

24

17.25

11.99

0.1445

0.6956

0.7188

0.5

1035

PV panel Power out


PV Fil l factor

Converter Power out

PV panel output current

PV cell output power

T

Fig. 6 (d) Generalized PVPC system model

2.4 Controller subsystem selection , modeling and design Different control approaches can be proposed to control the overall SEMRP system output performance in terms of output speed, as well as, controlling output characteristics and performance of PVPC subsystem to meet desired output voltage or current under input working operating conditions. PI controller: because of its simplicity and ease of design, PI controller is widely used in variable speed applications and current regulation, in this paper PI controller is selected for achieving desired outputs characteristics of PVPC subsystem and meeting desired output speed of overall SEMRP system, where Different PI controllers configurations are to be applied to control the PVPC subsystem and overall SEMRP system to achieve desired outputs of speed, voltage and load currents for particular SEMRP system application, it is important to notice that PI controller can be replace with PID or any other suitable control algorithm .

The PI controller transfer function in different forms is given by Eq.(41). The PI controller pole and zero will affect the response, mainly the PI zero given by; ZRoR=-KRIR/KRPR, will inversely affect the response and should be canceled by prefilter, while maintaining the proportional gain (KRPR), the prefilter transfer function is given by Eq.(42) , the placement of prefilter is shown on generalized model.

( )

( )

( )

( 1) 1( ) * * 1

IP

P I PIPI P

P o IPI PI PI

I I

KK sK s K KKG s K

s s sK s Z T sG s K K

s T s T s

+ + = + = = =

+ += = = = +

(41)

( ) ( )Pr ( ) O PIefilter

O PI

Z ZG ss Z s Z

= =+ +

(42)

PI controller with deadbeat response design, Deadbeat response means the response that proceeds rapidly to the desired level and holds at that level with minimal overshoot, The characteristics of deadbeat response include; Zero steady state error, Fast response, (short rise time and

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settling time) and minimal undershoot, ±2% error band [14-15] [28], Controller with deadbeat response design is described and designed in details in [14]. In [15] a MATLAB built-in function to calculate desired deadbeat parameters including KPI , ZPI is designed and proposed. 3. Proposed generalized Solar Electric Mobile Robotic Platform (SEMRP) system model Integrating all sub-models of all subsystems; particularly PV panel subsystem ,DC/DC buck converters subsystem, mobile platform subsystem, controller subsystem and load torque subsystem shown in Fig.s 3,4,5,6, will result in generalized SEMRP system model shown in Fig. 7(a), another generalized model can be proposed and shown in Fig. 7 (a) ( in next section). The inputs to the first model are operating conditions of PV panel; irradiation β, working temperature T, PV panel-array construction including series NRs Rand parallel NRm R cells and cell surface area A. The outputs of this model are numerical visual data, graphical data and output response curves of PV panel, converter and platform subsystems including; output linear speed, current, torque, acceleration, PV panel output current, volt, V-I and P-V Characteristics, finally, DC/DC converter output current and voltage. The generalized SEMRP system model is supported with different control algorithms including PID,PD,PI, PI with deadbeat response to control the mobile platform speed and performance, and can be modified to include any other control algorithm, also, also this model can be modified to include other control approaches to control PVPC subsystem outputs to match load requirements according to control approaches proposed in[25] including voltage and current control of PVPC

subsystem to match platform voltage and current requirements 4. Testing and analysis The proposed model works by defining the input operating condition and cells construction, based on this, the solar panel will generate corresponding output voltage , the DC/DC buck converter will reduce the input from PV panel voltage to platform voltage (e.g 12 Volts) according to duty cycle D , the resulted from PVPC subsystem volts are fed to mobile platform for motion, finally, the selected and designed controller is used to control the performance of mobile platform to meet desired response and desired output speed. Testing the proposed generalized model for desired output speed of 0.5 m/s for SEMRP subsystems parameters defined in Table-1, and under PV panel operating conditions of irradiation β=200, and T=50 and number of series NRsR=48 and parallel NRm R= 30, cell surface area A= 0.0025 mP

2P, and by

applying PI controller with deadbeat response design, using methodology discussed in [14] and MATLAB built-in function designed in [15], with PI speed controller, will result in maximum output numerical visual and graphical output readings that allow designer to 0Thave the maximum data to select,0T design, integrate, tested and analyze the overall SEMRP system and each subsystem, these data output are listed in Table-2 and shown in Fig. 7(a)(b)(c), including PV panel currents of 41.01 A, and voltage of 24 V, Converter's output voltage of 12.01 V , PV panel V-I and P-V Characteristics shown in Fig. 7(e)(f) , and Converter outputs current, voltages responses shown in Fig. 7 (g) , finally platform output linear speed of 0.5 m/s and responses shown in Fig. 7(h), as well as platform torque, current and acceleration shown in Fig. 7(i)

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PI C

ontro

ller

Conv

erte

r I o

ut

Con

verte

r V o

ut

PV p

anel

I ou

t

PV

pan

el V

out

r

n n

Jequ

iv g

Vin

12 V

m

Switc

h

Sign

al 1

Sign

al B

uild

er

rou

Ram

p

Ra

Zo s+Zo

Pref

ilter

.

1 1Pr

efilt

er

Pl

Duty

cyc

le

T Irrad

iation

, B

V Cell s

urfa

ce a

rea

A

Ns Np

PV p

anel

curre

nt o

ut

PV p

anel

Volt

out

Conv

erte

r I o

ut

Conv

erte

r V o

ut

PVPC

Sub

syste

m

PID(

s)

PID

Cont

rolle

r1

PI(s)

PI C

ontro

ller

PD(s)

PD C

ontro

ller

Out1

Mot

ion

prof

ile

Iner

tia (

mot

or+

load)

Inpu

t Volt

,(0 :1

2)

Gea

r rat

io,n

Tach

omet

er c

onst

ant ,

Kta

c

All v

iscou

s da

mpin

g

Arm

atur

e In

duct

ance

, L

Arm

atur

e Re

sista

nce

, R

Torq

ue c

onst

ant ,

Kt

whee

l rad

ius, r

M : T

he m

ass

of th

e m

obilr

robo

t

g: T

he g

ravi

ty a

ccele

ratio

n (m

/s2)

.

CL: T

he c

oeff

icien

t of l

ift,

( CL

to b

e 0

.10

or 0

.16)

B : m

obile

robo

t un

ders

ide a

rea

EMF

cons

tant

, Kb

Cd :

Aero

dyna

mic

drag

coe

ffici

ent

A:Cr

oss-

sect

ional

area

of m

obile

robo

t, wh

ere

it is

the

wide

st,

Rou:

The

invi

ronm

ent (

air)

den

sity

(kg/

m3)

Cr: T

he ro

lling

resis

tanc

e co

effic

ients

Pref

ilter

Cont

rolle

r

Torq

ue, T

outp

ut a

ngua

l sp

eed,

Om

ega

Curre

nt, I

spee

d in

mps

Out1

Out2

Mob

ile p

latfo

rm S

ubsy

stem

m

La

Ktac

h

Ktac

h

Kt

Kb

bequ

iv

Dam

p.

Cr

CL

Cd

refe

renc

e_ar

ea

front

_are

a

NsA NmV .2

s+Zo s ,1

B

su

n Irr

ad

D

Dut

y cyc

le, D

24

41.0

1

12.0

1

1.44

2

T

Kp

Fig. 7(a) Generalized Simulink model of SEMRP system

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Rolling resistance forceM*g*Cr*cos()

aerodynamics lift force

r*m/2r*m/2

angular speedTorque

current PI Controller

Coloum Friction

6Out2

5Out1

4speed in mps

3 Current, I

2output angual speed, Omega

1Torque, T

1wheel radius, V=W*r1

-K-

rads2mps=R_wheel*(2*pi)/(2*pi).

-K-

0.5

0.5

aerodaynamic torque,0.5*p*A*Cd*v^2

mobile_platform_.mat

sin(u)cos(u)

SinCos.

Saturation2Saturation1

Manual Switch

1s

Integrator9

1s

Integrator12

45

Inclination angle

Divide9

Divide8Divide7

Divide6

Divide5Divide4

Divide30

Divide3

Divide29

Divide28

Divide27

Divide26

Divide22

Divide21Divide2

Divide18Divide17

Divide16

Divide15

Divide14

Divide12

Divide11

Divide10Divide1

Divide,1

du/dt

-K-

Add32

1

1. 1

r/2..

0.5

.

s+Zo

s,1

1 ,

bm

1

Kp

20Controller

19 Prefilter

18Cr: The roll ing resistance coefficients

17Rou: The invironment ( air) density (kg/m3)

16A:Cross-sectional area of mobile robot, where it is the widest, (m2)

15Cd : Aerodynamic drag coefficient

14EMF constant, Kb

13B : mobile robot underside area

12CL: The coefficient of l ift, ( CL to be 0.10 or 0.16)

11g: The gravity acceleration (m/s2).

10M : The mass of the mobilr robot

9wheel radius, r

8Torque constant ,Kt

7Armature Resistance , R

6Armature Inductance, L

5 All viscous damping

4 Tachometer constant , Ktac3 Gear ratio,n

2Input Volt,(0 :12)

1 Inertia (motor+ load)

Fig. 7(b) Sub-model of DC machine with load torques

Vin

Vout

Cell power

4Converter V out

3Converter I out

2PV panel Volt out


PV_con8.mat

PV_con7.mat

PV_con6.mat

PV_con5.mat

PV_con4.mat

PV_con.mat

PV_con3.mat

PV_con2.mat

PV_con12.mat

PV_con10.mat

PV_con9.mat

PV_con1.matDuty cy cle

T

Irradiation, B

V


Ns

Np

Conv erter current out

Conv erter v oltage out

Volatges comparision

Conv erter Power out

PV panel Volt out


PV cell Volt out

PV cell current out

PV cell Power in

PV cell Power out

PV cell ef f iciency

Fill Factor

PV panel Power out

PV-Converter Subsystem

PV panel power in

PV cell output volt


PV cell efficiency

[Cell_Vout]

[panel_Vout]

[Cell_Vout]

[Cell_Iout]

Cell P-V

Cell I-V

,.

12.01

24

System Vin-Vout comparision

Converter current Iout

1.442

Converter Volt Iout

35.45

0.5

1064

24

17.33

12.01

3.563

0.02821

17.73

0.5

553e+004

PV panel Power out


PV Fil l factor

Converter Power out

PV panel output current

PV cell output power

7Np

6Ns

5Cell surface

area A

4V

3Irradiation, B

2T

1Duty cycle

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Fig. 7(c) Both subsystems of PVPC system models united in One sub-model

Pout

13PV panel Power out

12Fill Factor

11PV cell efficiency

10PV cell Power out

9PV cell Power in

8 PV cell current out

7PV cell Volt out


5PV panel Volt out

4Converter Power out

3Volatges comparision

2Converter voltage out

1Converter current out

Terminator

Product



T

B

V

A

Ns

Np

Panel V out

Panel I out

Cell Vout

Cell I out

Cell Power in

Cell Power out

Cell Ef f iciency

Fill Factor

PV Panel Subsystem

Duty cy cle, D

Vin

Vc

IL

Vo

Buck converter Subsystem

''1

7Np

6Ns

5Cell surface

area A

4V

3Irradiation, B

2T

1Duty cycle

Fig. 7(d) Three sub-models of PVPC subsystem; panel, converter and PWM sub-models

Table 2 Simulation results of each subsystem and whole system PVPC system

inputs PV cell outputs PV Panel outputs Converter outputs SEMRP outputs

β 200 Voltage 0.5 V Voltage 24 V Voltage 11.99 V Linear Speed 0.5 T 50 Current 1.438 A Current 43.134A Current 1.439 A Angular.

Speed. 6.65

D 0.5 Fill factor 0.1445 Power out

17.25 motor Torque

7.021

A 0.0025 Power out 0.7188 Current 5.909 Ns 48 Power in 0.5 Np 30 Efficiency 0.6956

Fig. 7 (e) V-I Characteristics for β=200, and T=50 Fig. 7 (f) P-V Characteristics for β=200, and

T=50

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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-5

0

5

10

15

20

25

Time (s)

Mag

nitu

de ;

I , V

Model readings PV_Vout , Conv_Vout, Conv_Iout

Converter output current Iout

Converter output Voltage Vout

Input Voltage to Converter; PV_Vout

Fig. 7 (g) Inputs-outputs data of DC/DC Converter subsystem

0 1 2 3 4 5 6 7 8 9 10-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time (s)

m

Platform linear speed

0 2 4 6 8 10 12 14-1

0

1

2

3

4

5

6

7

8

Time(s)

Mag

nitu

de

SEMRP system outputs

linear speed

Angular speed

DC machine current

DC machine torque

Fig. 7 (h) platform's output linear speed vs. time response

Fig. 7 (i) platform's output current, torque, speed, acceleration vs. time responses

4.1 Controller selection and design for specific purpose The proposed generalized model can be modified to include different control algorithms to control PVPC subsystem performance and output characteristics, including controlling output current to match load-current, controlling output voltage to match load-voltage , controlling both output voltage and current to meet load requirements. In [25] different control approaches are applied and tested to control the performance and characteristics of the PVPC subsystem. In this paper controlling both PVPC subsystem current and voltage to meet load-platform desired voltage and current is to be applied, while achieving desired output speed using PI controller 4.2 Controlling both PVPC subsystem current and voltage to meet SEMRP load-platform system desired

voltage and current, while achieving desired output speed. The proposed control approach of the overall SEMRP system will have the configurations shown in Fig. 8 (a). PI controller and with prefilter and deadbeat response design, are used to control the mobile platform output linear speed to meet 0.5 m/s and 1 m/s, two control approaches are used to current and voltage control to meet desired platform load-current and voltage. Matching load-platform desired current ; as shown in Fig. 8 (c) the comparison between load's and converter's currents is used to match the both currents, where load-platform current Iload is fedback to converter and compared with the converter output current Iconv, the difference is used to match the desired output platform current, according to the duty cycle D. Controlling the converter's output voltage to meet desired platform voltage: as shown in Fig. 8 (b), The desired

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converter output voltage and the converter actual output voltage are compared to calculate the error signal, used by PI controller to drive the converter switch according to the calculated duty cycle to meet platform voltage, The duty cycle D cycle is calculated automatically, as the ratio of converter's voltage to desired output voltage, and given by Eq.(43).

__ _

_

Conv out desired

Panel out

VD

V= (43)

Testing the proposed model for desired converters output voltage ,VRout_desiredR= 12 V and desired linear speed of 1 m/s, at irradiation β= 200 and temperature T=75, for SEMRP system parameters values defined in table-1, will result in liner speed of1 m/s and currents, torque and acceleration shown in Fig. 8 (d)(e), and matching all currents (load-platform current, converter output current) to have the value of 10.45 A, as well as, matching all volts to be 12 V. Also, running the model, will result in all data required to analyze the

SEMRP system performance and outputs characteristics, including converter output volts of 12 V, PV panel output voltage of 24 V, and duty cycle of D=0.5 ,and I-V, and P-V characteristics, these values and other are numerically shown in Fig. 8 (a), the plots of PV panel output voltage, converter output voltage and converter output current are shown in Fig. 8 (d), the control signal is shown in Fig. 8 (e). The proposed model can be modified to include PI current controller, where converter output current and DC motor armature current are compared and the different is used by PI current controller to control and ensure that the required load-platform current is met, the proposed control approach is shown in Fig. 8(f), running this model will result in same outputs shown in Fig. 8(c)(d)(e)(f)

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PI Co

ntroll

er

Conv

erter

I out

Con

verte

r V ou

t

PV pa

nel I

out

PV p

anel

V out

r

n n

[Conv

_Vou

t]

[pane

l_Vou

t]

[moto

r_curr

ent]

motor

curre

nt

Jequ

iv g

V_ou

t_desi

red

Vout

desire

d

Vin 12

V

Switc

h

Signa

l 1

Signa

l Buil

der

rou

Ramp

Ra

Zo s+Zo

Prefilt

er.

1 1Pre

filter

Duty

cycle

T Irradia

tion,

B

V Cell s

urfac

e are

a A

Ns Np Load

curre

nt

PV pa

nel c

urren

t out

PV pa

nel V

olt ou

t

Conv

erter

I out

Conv

erter

V out

PVPC

Subsy

stem

PID(s)

PID Co

ntroll

er1

PI(s)

PI Co

ntroll

er1

PI(s)

PI Co

ntroll

er

PD(s)

PD Co

ntroll

er

Out1

Motio

n prof

ile

Inertia

(moto

r+ loa

d)

Input

Volt,(

0 :12

)

Gea

r ratio

,n

Tach

omete

r con

stant

, Ktac

All vi

scou

s dam

ping

Armatu

re In

ducta

nce,

L

Armatu

re R

esist

ance

, R

Torqu

e con

stant

,Kt

whee

l radiu

s, r

M : T

he m

ass o

f the

mob

ilr rob

ot

g: Th

e grav

ity ac

celer

ation

(m/s2

).

CL: T

he co

efficie

nt of

lift, (

CL t

o be

0.10 o

r 0.16

)

B : m

obile

robot

unde

rside

area

EMF c

onsta

nt, Kb

Cd : A

erody

nami

c drag

coeff

icient

A:Cros

s-sec

tiona

l area

of m

obile

robot,

where

it is

the wi

dest,

Rou:

The i

nviro

nmen

t ( air

) den

sity (

kg/m

3)

Cr: T

he ro

lling r

esist

ance

coeff

icients

Prefilt

er

Contr

oller

Conv

erter

I out

Torqu

e, T

outpu

t ang

ual s

peed

, Ome

ga

spee

d in m

ps

Out1

Out2

DC m

achin

e Curr

ent, I

Load

Curr

ent, I

Mobil

e plat

form

Subsy

stem

m

La

Ktach

Ktach

Kt

[Conv

_Vou

t]

[pane

l_Vou

t]

[Conv

_curr

ent]

Kb

bequ

iv

Damp

.

1.007

0.5 0.5

D calc

ulated

Cr

CL

Cd

refere

nce_

area

front_

area

NsA NmV .2

s+Zo s ,1

PV_c

on11

.mat

4[D]

[contr

ol]

B

sun

Irrad

[D] [contr

ol]

24

7513 12

10.53

T

Kp

Fig. 8(a) proposed control approach for Controlling both PVPC subsystem current and voltage to meet SEMRP load-platform

system desired voltage and current.

current

7Load Current, I

6 DC machine Current, I

1Torque, T

rm_.mat

1s

Integrator12

[motor_current]

Divide30

Divide29

Divide27

Divide26

Divide

10.53

10.53

21

Converter I out

8Torque constant ,Kt

7

Armature Resistance , R

6Armature Inductance, L

1 Inertia (motor+ load

Fig. 8 (b) a part of DC machine subsystem showing platform and converter currents

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Converter I out

Converter V out

PV panel I out

PV panel V out

[Conv_Vout]

[panel_Vout]

[motor_current]

motor current

V_out_desired

Vout desired

Duty cy cle

T

Irradiation, B

V


Ns

Np

Load current


PV panel Volt out

Conv erter I out

Conv erter V out

PVPC Subsystem

PI(s)

PI Controller1

[Conv_Vout]

[panel_Vout]

[Conv_current]

1.007

0.5

D desired

0.5

D calculated

Ns

A

Nm

V

.2

PV_con11.mat

4[D]

[control]

B

sun Irrad

[D]

[control]

24

7513

12

10.54

T

Fig. 8 (c) a part of DC machine subsystem showing platform and converter currents

Fig. 8 (c) Comparing load-platform and converters currents to match load current

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0 5 10 15-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (s)

m

Platform linear speed

0 2 4 6 8 10 12

-2

0

2

4

6

8

10

12

14

Time(s)

Mag

nitu

de

SEMRP system outputs

linear speed

Angular speed

DC machine current

DC machine torque

Fig. 8 (d) platform output linear speed Fig. 8 (d) platform output speed, current , torque and

acceleration VS time

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.2

0.4

0.6

0.8

1

Time (s)

Mag

nitu

de

Control signal

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

5

10

15

20

25

Converter output current; Iout

Converter output Voltage; Vout

Input Voltage to Converter; PV_Vout

X: 0.324Y: 12

Time (s)

Mag

nitu

de ;

I , V

Model readings PV_Vout , Conv_Vout, Conv_Iout

Fig. 8 (f) Control signal of PI controller Fig. 8 (e) PVPC subsystem output readings ;voltage, converter

output voltage and current

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PI Controller

Converter I out

Converter V out

PV panel I out

PV panel V out

[motor_current]

[Conv_Vout]

[panel_Vout]

[Conv_current]

V_out_desired

Vout desired

Ramp

Z

s+Pre

Pre

Duty cy cle

T

Irradiation, B

V


Ns

Np

Load current


PV panel Volt out

Conv erter I out

Conv erter V out

PVPC Subsystem

PID(s)

PID Controller1

PI(s)

PI Controller2

PI(s)

PI Controller1

PI(s)

PI Controller

PD(s)

PD Controller

Out1

Motion profile

[panel_Iout]

[Conv_Vout]

[panel_Vout]

[Conv_current]

1.007

0.5

D desired

0.5

D calculated

Ns

A

Nm

V

.2

s+Zo

s,1

PV_con11.mat

4[D]

[control]

B

sun Irrad

[D]

[control]

24

7513

12

10.54

-6.564e-006

T

Kp

Fig. 8 (f) a part of generalized model showing control approaches of PVPC subsystem, using two separate PI current and

voltage controllers .

4.3 Matching Photovoltaic Panel–Converter (PVPC) subsystem' current with platform's-load's current while achieving desired output speed. The proposed control approach and the overall SEMRP system will have the configurations shown in Fig. 9(a). PI controller with prefilter and deadbeat response design, are used to control the mobile platform output speed, the PV panel subsystem is given as a function of (V,Iload) = f(V,G,T) , with input current, irradiation and working temperature , in the proposed load-current control approach the platform armature current is fed to PV panel and used to generate the output voltage and current of PV panel- converter subsystem. That will be fed to DC machine to generate desire torque to overcome load torque.

Testing the proposed model shown in Fig. 7 (a), by applying PI Controller with deadbeat response design, for SEMRP system with all subsystems' parameters defined in tablel including duty cycle of D=0.5, under operating conditions of PV panel; irradiation β=200, and T=50 for desired output linear speed of 1 m/s, and PVPC subsystem' output voltage of 12 V. will result in match desired load-platform current to overcome load-torque and in all, numerical visual and graphical data required, (shown in Fig. 9(a)(b)(c)), as well as, output platform's linear speed of 0.9994 m/s , platform-load's current of 17.17 A, that is equal to converter output current of 17.17 A , and converter's output volt of 12 V, for PV panel output voltage of 24 V, and finally, V-I and P-V Characteristics of PV panel shown in Fig. 9(e)(f).

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angular speed

Current,i

Torque

EMF constant Kb

PI Controller

Torque

l inear acceleration.

linear speed.

Angular Speed Converter I out

Converter V out

PV panel I out

PV panel V out

Kt

torqueconstant

-K-

rad2mpsV=W*r1

[motor_current]

motor current

1/n

gear ration=3.1

1

La.s+Ra


1

den(s)


Torque

Step,V=12,

-K-

Speed feedbacK, Ktach

Kb

Zo

s+ZoPrefilter

Duty cy cle

T

Irradiation, B

V


Ns

Np

Load current


PV panel Volt out

Conv erter I out

Conv erter V out

PVPC Subsystem

Inclination angle

Angular speed

Load torque


Inclination

Inclination angle

[Conv_current]

[motor_current]

[Conv_current]

du/dt

Current.

Mobile_robot6.mat

Ns

A

Nm

V

.2

Mobile_robot5.mat

.1

Mobile_robot2.maMobile_robot3.mat

Mobile_robot7.mat

.

s+Zo

s,

B

sun Irrad

D

Duty cycle, D

15.17 18.03 0.9983

13.31

24

7513

11.9

15.17

15.17

-0.02425

64.56

T

Kp

Fig. 9(a) proposed current control approach using second generalized model

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Line

ar s

peed

M

SEMRP linear speed

0 1 2 3 4 5 6

-5

0

5

10

15

20

Time (s)

LMag

nitu

de

SEMRP outputs; Speed, Current, Torque Acceleration

Angualr speed

linear speed

current

torque

Fig. 9(b) SEMRP system output linear speed VS time applying currents comparison and PI controller with

deadbeat response

Fig. 9(c) SEMRP system output current, speed, torque and angular acceleration all VS time applying currents

comparison and PI with deadbeat response

4.4 PI Controller for only speed performance control of SEMRP system in direct-coupling to the PVPC subsystem. The overall SEMRP system will have the configurations shown in Fig. 10(a). In the proposed model, PI controller with deadbeat response is used to control the mobile platform output speed, no control is applied to control the PVPC subsystem output characteristics and performance. Applying PI Controller with deadbeat response design, for subsystems parameters defined in Tablel-1 , under same operating conditions of PV panel, will result in numerical visual and graphical data and response curves shown in

Fig. 10(a)(b), including V-I and P-V Characteristics of PV panel shown in Fig. 7(d)(e), the simulation and response curves show that under the given input operating condition, the solar panel will generate 24 Volts, the DC/DC buck converter will reduce the input from PV panel voltage to almost 12 Volts according to duty cycle of 0.5 , the resulted from PVPC subsystem 12 volts are fed to mobile platform to move, and PI controller with prefilter are used to control the performance of mobile platform to meet deadbeat response and meet desired 0.5 m/s output, a soft tuning of deadbeat controller parameters will soften the response.

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angular speedCurrent,i

Torque

EMF constant Kb

PI Controller

Torque

l inear acceleration.

linear speed.

Angular Speed

PV panel V out

PV panel I out

Converter V out

Converter I out

Kt

torqueconstant

-K-

rad2mpsV=W*r1

1/n

gear ration=3.1

1

La.s+Ra


1

den(s)


Torque

Step,V=12,

-K-

Speed feedbacK, Ktach

Kb

Zo

s+ZoPrefilter

Duty cy cle

T

Irradiation, B

V


Ns

Np


PV panel Volt out

Conv erter I out

Conv erter V out

PVPC Subsystem

Inclination angle

Angular speed

Load torque

Load torque sub-system45

Inclination angle

du/dt

Current.

Mobile_robot4.mat

Ns

A

Nm

V

.2

Mobile_robot.mat

Mobile_robot2.maMobile_robot3.mat Mobile_robot1.mat

.

s+Zo

s,

B

sun Irrad

D

Duty cycle, D

2.063 2.451

0.4995

6.66

24

8359

11.99

1.439

0

6.62

T

Kp

Fig. 10(a) proposed model of SEMRP system control applying PI with deadbeat

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

X: 2.975Y: 0.5007

Time (s)

Lin

ear s

peed

SEMRP linear speed

0 1 2 3 4 5 6 7 8 9 10

-3

-2

-1

0

1

2

3

4

5

6

7

Time (s)

Mag

nitu

de

SEMRP output readings

Angualr speed

linear speed linear accel.

current torque

Fig. 10(d) SEMRP system speed VS time applying PI

with deadbeat

Fig. 10(e) SEMRP system output current, speed, torque and angular acceleration all VS time applying PI with

deadbeat response

5. CONCLUSIONS A generalized and refined model for Mechatronics design of Solar Electric Mobile Robotic Platforms (SEMRP) systems is proposed and tested, the proposed model consists of five main subsystems’ sub-models, and is developed to allow designer to 0Thave the maximum output data to 0Tdesign, tested and analyze the overall SEMRP system and each subsystem, for desired overall and/or

either subsystem's outputs under various PV subsystem operating conditions, to meet particular SEMRP system requirements and performance. the whole SEMRP system model and each subsystems model, are tested, analyzed and evaluated0T for desired system requirements and performance in Matlab/Simulink, t0The obtained results show the simplicity, accuracy and applicability of the presented models in Mechatronics design of SEMRP system

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applications, as well as, for application in educational process. Table 1 Nomenclature and nominal characteristic of SEMRP subsystems

DC machine parameters

Vin=12 V Input voltage to DC machine Kt=1.188 Nm/A

Motor torque constant

Ra = 0.156 Ω

Motor armature Resistance

La=0.82 MH Motor armature Inductance, Jm=0.271 kg.m2

Geared-Motor Inertia

bm=0.271 N.m.s

Viscous damping

Kb=1.185 rad/s/V

Back EMF constant,

n=1 Gear ratio r=0.075 m, Wheel radius Jequiv kg.m2 The total equivalent inertia, bequiv N.m.s The total equivalent damping, L=0.4 m The distance between wheels centers K tac=12/6.667=1.8 rad/s

Tachometer constant,

ω=speed/r, rad/s

=0.5/0.075=6.667 ,also 1/0.075=13.3333

Tshaft The torque produced by motor η The transmission efficiency Tshaft The torque, produced by the driving

motor

Nominal values for Mobile platform M,m, Kg The mass of the mobile platform CRd R=0.80 Aerodynamic drag coefficient CRL The coefficient of lift, with values( CRLR to

be 0.10 or 0.16), Cr=0.5 The rolling resistance coefficient ρ , kg/mP

3 The air density at STP, ρ =1.25 a, m/sP

2 Platform linear Acceleration G, m/sP

2 The gravity acceleration Ν, m/s The vehicle linear speed. α , Rad Road slope or the hill climbing angle B Mobile platform's reference area L lift, ARf Platforms frontal area KRP Proportional gain KRI Integral gain ZR0 PI controller zero PRm The power available in the wheels of

the vehicle. TRTotalR The total resistive torque, the torque of

all acting forces. Solar cell parameters

Isc=8.13 A , 2.55 A , 3.8

The short-circuit current, at reference temp 25 P

◦PC

I A The output net current of PV cell (the PV module current)

IRph R A The light-generated photocurrent at the nominal condition (25 P

◦PC and 1000

W/mP

2P),

ERg R : =1.1 The band gap energy of the semiconductor

/tV KT q= The thermo voltage of cell. For array :( /t sV N KT q= )

IRsR ,A The reverse saturation current of the diode or leakage current of the diode

Rs=0.001 Ohm The series resistors of the PV cell, it they may be neglected to simplify the analysis.

Rsh=1000 Ohm The shunt resistors of the PV cell V The voltage across the diode, output q=1.6e-19 C The electron charge BRoR=1000 W/mP

2 The Sun irradiation β =B=200 W/mP

2 The irradiation on the device surface

Ki=0.0017 A/◦C The cell's short circuit current temperature coefficient

Vo= 30.6/50 V Open circuit voltage Ns= 48 , 36 Series connections of cells in the

given photovoltaic module Nm= 1 , 30 Parallel connections of cells in the

given photovoltaic module K=1.38e-23 J/oK;

The Boltzmann's constant

N=1.2 The diode ideality factor, takes the value between 1 and 2

T= 50 Kelvin Working temperature of the p-n junction

TRrefR=273 Kelvin The nominal reference temperature

Buck converter parameters

C=300e-6; 40e-6 F

Capacitance

L=225e-6 ; .64e-6 H

Inductance

Rl=RL=7e-3 Inductor series DC resistance rc= RC=100e-3 Capacitor equivalent series resistance,

ESR of C , VRinR= 24 V Input voltage R=8.33; 5 Ohm;

Resistance

Ron=1e-3; Transistor ON resistance

KD=D= 0.5, 0.2,

Duty cycle

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Tt=0.1 , 0.005 Low pass Prefilter time constant VL Voltage across inductor IC Current across Capacitor

REFERENCES [1] 2TFarhan A. Salem, Ahmad A. Mahfouz 0T2T , 0TA

Proposed Approach to Mechatronics Design and Implementation Education-Oriented, Innovative Systems Design and Engineering , Vol.4, No.10, pp 12-39,2013.

[2] Stephen Se, David Lowe ,Jim Little, Mobile Robot Localization and Mapping with Uncertainty using Scale-Invariant Visual Landmarks, The International Journal of Robotics Research, Vol. 21, No. 8, August 2002, pp. 735-758,2002

[3] J. Borenstein, B. Everett, and L. Feng. Navigating Mobile Robots: Systems and Techniques. A. K. Peters Ltd, Wellesley, MA, 1996.

[4] A.J. Davison and D.W. Murray. Mobile robot localisation using active vision. In Proceedings of Fifth European Conference on Computer Vision (ECCV'98) Volume II, pages 809{825, Freiburg, Germany, June1998.

[5] H. Andreasson, A. Treptow, and T. Duckett. Localization for mobile robots using panoramic vision, local features and particle filter. In Proc. of the IEEE Int. Conf. on Robotics & Automation (ICRA), 2005..

[6] D. Brˇsˇci´c and H. Hashimoto. Comparison of robot localization methods using distributed and onboard laser range finders. In IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, 2008.

[7] J. Borenstein,, H.R. Everett,, L. Feng,, and D. Wehe,Mobile Robot Positioning and Sensors and Techniques, Invited paper for the Journal of Robotic Systems, Special Issue on Mobile Robots. Vol. 14 No. 4, pp. 231 – 249.

[8] Barshan, B. and Durrant-Whyte, H.F., 1995, “Inertial Navigation Systems Mobile Robots.” IEEE Transactions on Robotics and Automation, Vol. 11, No. 3, June, pp. 328-342.

[9] Borenstein, J., Everett, B., and Feng, L., 1996b, “Navigating Mobile Robots: Systems and Techniques.”, A. K. Peters, Ltd., Wellesley, MA, ISBN 1-56881-058-X.

[10] PeLoTe Session,Mobile Robots for Search and Rescue, Proceedings of the 2005 IEEE International Workshop on Safety, Security and Rescue Robotics Kobe, Japan, June 2005.

[11] J. Kuhle, H. Roth, and N. Ruangpayoongsak, “mobile robotics and airships in a multi-robot team,” The 1st IFAC Symposium on Telematics Applications in Automation and Robotics, Helsinki University of Technology, Finland, pp. 67-72, June 2004.

[12] Farhan A. Salem ,Dynamic and Kinematic Models and Control for Differential Drive Mobile Robots, International Journal of Current Engineering and Technology, Vol.3, No.2 (June 2013)

[13] 2TFarhan A. Salem, Ahmad A. Mahfouz 0T2T , 0TA Proposed Approach to Mechatronics Design and Implementation Education-Oriented, Innovative Systems Design and Engineering , Vol.4, No.10, pp 12-39,2013.

[14] Farhan A. Salem, Refined modeling and control for Mechatronics design of mobile robotic platforms, Estonian Journal of Engineering, 19, 3, 212–238,2013.

[15] Farhan A. Salem, Mechatronics motion control design of electric machines for desired deadbeat response specifications, supported and verified by new MATLAB built-in function and Simulink model, submitted to European journal 2013 .

[16] Ahmad A. Mahfouz, Ayman A. Aly, Farhan A. Salem , Mechatronics Design of a Mobile Robot System, I.J. Intelligent Systems and Applications, 03, 23-36, 2013.

[17] Ahmad A. Mahfouz, Mohammed M. K., Farhan A. Salem , Modeling, Simulation and Dynamics Analysis Issues of Electric Motor, for Mechatronics Applications, Using Different Approaches and Verification by MATLAB/Simulink (I). I.J. Intelligent Systems and Applications,pp39-57 ,05, 39-572013,

[18] Farhan A. Salem, mobile robot dynamics analysis and control , 4TVI Международная научно-практическая конференция 4T , 3T«Инженерные системы - 2013».

[19] Jaroslav Hanzel , Ladislav Jurišica , Marian Kľúčik , Anton Vitko , Matej Strigáč, Experimental mobile robotic system

[20] Bashir M. Y. Nouri , modeling and control of mobile robots, Proceeding of the First International Conference on Modeling,

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Simulation and Applied Optimization, Sharjah, U.A.E. February 1-3, 2005.

[21] Wai Phyo Aung, Analysis on Modeling and Simulink of DC Motor and its Driving System Used for Wheeled Mobile Robot, World Academy of Science, Engineering and Technology 32 2007

[22] Mircea Niţulescu, solution for modeling and control in mobile robotics, control engineering and applied informatics -CEAI,, Vol. 9, No. 3;4, pp. 43-50, 2007

[23] Farhan A. Salem, ’Modeling and Simulation issues on Photovoltaic systems, for Mechatronics design of solar electric applications, IPASJ International Journal of Mechanical Engineering (IIJME),Volume 2, Issue 8, August 2014.

[24] Farhan A. Salem, New generalized Photovoltaic Panel-Converter system model for Mechatronics design of solar electric applications, IPASJ International Journal of Mechanical Engineering (IIJME),Volume 2, Issue 8, August 2014.

[25] Farhan A. Salem, Photovoltaic-Converter system, modeling and control issues for Mechatronics design of

solar electric application, I.J. Intelligent Systems and Applications, 08,2014,

[26] Farhan A. Salem, Mechatronics Design of Motion Systems; Modeling, Control and Verification , International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:13 No:02 , 2013.

[27] Farhan A. Salem, Dynamic Modeling, Simulation and Control of Electric Machines for Mechatronics Applications, international journal of control, automation and systems Vol.1 No.2, pp30-41, April, 2013.

[28] Richard C. Dorf and Robert H. Bishop, Modern Control Systems, Ninth Edition, Prentice-Hall Inc., New Jersey, 2001.

[29] Farhan A. Salem, Mechatronics Design of Solar Tracking System, International Journal of Current Engineering and Technology, Vol.3, No.2 (June 2013)

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