Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 555 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 556 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 557 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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)
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 558 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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,
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 559 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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):
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 560 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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)
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 561 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
Load torque subsystem
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)
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 562 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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).
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 563 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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]
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 564 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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]
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 565 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
Duty cy cle, D switchin signal (0,1) PWM
PWM Generator Subsystem
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
,.
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 566 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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 cell output current
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 567 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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)
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 568 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 569 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
1PV panel current 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
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]
[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 cell output current
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 570 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
6PV panel current out
5PV panel Volt out
4Converter Power out
3Volatges comparision
2Converter voltage out
1Converter current out
Terminator
Product
Duty cy cle, D switchin signal (0,1) PWM
PWM Generator Subsystem
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 571 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 572 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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)
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 573 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 574 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
Cell surf ace area A
Ns
Np
Load current
PV panel current out
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 575 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 576 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
Cell surf ace area A
Ns
Np
Load current
PV panel current out
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).
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 577 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
Transfer function1/(Ls+R)
1
den(s)
Transfer function1/(Js+b).
Torque
Step,V=12,
-K-
Speed feedbacK, Ktach
Kb
Zo
s+ZoPrefilter
Duty cy cle
T
Irradiation, B
V
Cell surf ace area A
Ns
Np
Load current
PV panel current out
PV panel Volt out
Conv erter I out
Conv erter V out
PVPC Subsystem
Inclination angle
Angular speed
Load torque
Load torque subsystem
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.
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 578 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
Transfer function1/(Ls+R)
1
den(s)
Transfer function1/(Js+b).
Torque
Step,V=12,
-K-
Speed feedbacK, Ktach
Kb
Zo
s+ZoPrefilter
Duty cy cle
T
Irradiation, B
V
Cell surf ace area A
Ns
Np
PV panel current out
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 579 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 580 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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,
IJSER
International Journal of Scientific & Engineering Research, Volume 5, Issue 8,August-2014 581 ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
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)
IJSER