Mechatronics Design of Motion Systems; Modeling, Control ... · PDF fileMechatronics Design of Motion Systems; Modeling, Control and Verification. Farhan A. Salem1,2 1Mechatronics

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:13 No:02 1

131402-6565-IJMME-IJENS © April 2013 IJENS I J E N S

Abstract-- To help in facing the two top challenges in

developing mechatronic systems, while maintaining desired

accuracy and to optimize system level performance to meet the

design requirements, this paper proposes an accurate

mathematical and simulink models for accurate mechatronics

design and verification of both system and control of motions

throughout Mechatronics systems design and development

process, including proper selection, analysis, integration and

verification of the overall system and sub-systems performance

in terms of output speed, angle, torque, current, acceleration

and signals, resulting in simplifying and accelerating

Mechatronics systems design process. The proposed models

intended to be used for research purposes in mechatronics

motion systems design, motion control applications, as well as,

for the application in educational process. The proposed model

can be modified to include any control strategy and/or any

actuator. The model was created and verified using MATLAB

simulink software

Index Term— Mechatronics system, Motion control,

Mathematical and simulink function block models.

I. INTRODUCTION

Mechatronics system design is Modern interdisciplinary

design procedure; it is a concurrent selection, integration and

optimization of the system and all its components as a whole

and concurrently, all the design disciplines work in parallel and

collaboratively throughout the design and development

process to produce an overall optimal design. Mechatronics

design approach tends to develop products with synergy and

integration toward constrains like higher performance, speed,

precision, efficiency, lower costs and functionality. The two

top challenges faced in developing mechatronic systems are

the early identifying system level problems and ensuring that

all design requirements are met, in order to evaluate concepts

generated during the design process, without building and

testing each one, mechatronics engineer, must be skilled in

modeling, simulation, analysis, and control of dynamic systems

and understand the key issues in hardware implementation [1-

6].

Motion control is a sub-field of control engineering, in which

the position or velocity of a given machine are controlled using

some type of actuating device. Most used actuating devices

in mechatronics applications are electric actuating machines,

which are used in many, if not most, modern machines (e.g.

electric cars, locomotives, fans, turbines, and drills), robotics

(e.g. Mobile robot and robot arm), industrial and

manufacturing (e.g. conveyer belts, rolling, cutting, welding,

saws and bending machines as well as to spin gears and food

and medical industry mixers), also, many kitchen appliances

use DC motors. Two main motion control applications are of

concern; mobile robots and robot arms.

Accurate control of motion is a fundamental concern in

mechatronics applications, where placing an object in the

exact desired location with the exact possible amount of force

and torque at the correct exact time, while consuming minimum

power, at minim cost, is essential for efficient system operation,

while maintaining accuracy, to simplify and accelerate

Mechatronics systems design process, and considering the

two top challenges faced in developing mechatronic systems,

including proper selection, analysis, integration and

verification of the overall system and sub-systems

performance throughout the development process, and

optimize system level performance to meet the design

requirements, this paper proposes an accurate general

mathematical and simulink models of system, motions and

control in mechatronics applications, in terms of output speed ,

angle, torque, current, acceleration and signals , in terms of best

selection and integration of system's mechanical parts,

controller and components, as an application example the

proposed model will be tested in mechatronics design of two

systems a mobile robotic platform and robotic arm systems,

where an electric motor, a motion control system and

corresponding components are selected, designed and

integrated to move a given mechanical system to/with a

desired output (speed and/or position), corresponding to

applied input voltage ,Vin, achieving and maintaining all design

requirements.

Mechatronics Design of Motion Systems;

Modeling, Control and Verification.

Farhan A. Salem1,2

1Mechatronics program,. Dept. of Mechanical Engineering, Faculty of Engineering, Taif University, 888, Taif,

Saudi Arabia. 2 Alpha Center for Engineering Studies and Technology Researches, Amman, Jordan.

Email: [email protected]



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. 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 as well as the controller should be designed to make the

system robust and adaptive, improving the system on both

dynamic and steady state performances [1].Single joint robot

arm system consists of three main parts; arm, connected to

actuator through gear train.

The following nominal values for the various parameters of two

different eclectic motor can be used and tested: First motor:

Vin=12 Volts; Jm=0.02 kg·m²; bm =0.03;Kt =0.023 N-m/A; Kb

=0.023 V-s/rad; Ra =1 Ohm; La=0.23 Henry; TLoad, gear ratio,

for simplicity ,n=1. Second motor: Vin=12 Volts; Motor torque

constant, Kt = 1.1882 Nm/A; Armature Resistance, Ra =

0.1557 Ohms (Ω) ; Armature Inductance, La = 0.82 MH

;Geared-Motor Inertia: Jm = 0.271 kg.m2, Geared-Motor Viscous

damping bm = 0.271 Nms; Motor back EMF constant, Kb =

1.185 rad/s/V, gear ratio, for simplicity , n=1, 10.

The robot arm system to be designed, has the following

nominal values; arm mass, M= 8 Kg, arm length, L=0.4 m, and

viscous damping constant, b = 0.09 N.sec/m. so that a voltage

range of 0 to 12 volts corresponds linearly of an Robot arm

output angle range of 0 to 180, that is to move the robot arm to

the desired output angular position, θL , corresponding to the

applied input voltage ,Vin . The mobile robot system to be

designed, has the following nominal values wheel radius r

=0.075 m, wheelchair height,h= 0.920 m, wheelchair width ,b =

0.580 m, the distance between wheels centers = 0.4 m, The

most suitable linear output speed of used, domestic, mobile

robot is to move with 0.5 meter per second, (that is ω=V/r =

0.5/ 0.075 = 6.6667 rad/s,) . Tachometer constant, Ktac = 12 /

6.6667=1.8 (rad/sec)

II. SYSTEM MODELING

We are to model overall systems and sub-systems including

mechanical system, actuator, system dynamics, control

systems and sensors. The control of mechatronics system's

motion is simplified to electric machines motion control that

may or not include gear sys tem . Motion control system and

components , A negative closed loop feedback control system

with forward controller and corresponding simulink model

shown in Fig.1 are to be used. Electric machine is powered and

desired output movements will rely on how the electric motor is

commanded, by using a simple controller of e.g. PIC

microcontroller, and corresponding feedback element,

interfaces and electric machine, the output movements (the

rotation to a fixed speed or angle) can be controlled easily.

Different researches on this theme, can be found, most of it

study separate systems and control design. In [14] modeling,

simulation and analysis of the basic open loop DC motor

system using different approaches; different simplified and

accurate models are derived for different application. In [15]

analysis of how to choose DC motor to be balance with their

applications for a given mobile robot, also, specification of DC

Motor that can be used with desire mobile robot is determined

using MATLAB Simulink model. In [16] an accurate general

purpose mobile robotic platform for system and controller,

selection, design, modeling, testing and validation. In [17] a

model and control of mobile robots are presented. [18]

Addresses mechatronics design, modeling, controller

selection, design, simulation and analysis issues of a simple

robot arm considering all the forces applied upon the system.

In [18] a proposed mechatronics design including modeling

and control selection are introduced.

Meanwhile Mobile system dynamics depends on dynamics

between the surface, wheels and mobile platform, robot arm

dynamics depends on arm's mass, length and shape. The

geometry of the mechanical part determines the moment of

inertia, for simplicity, the mobile platform can be considered to

be of the cuboide or cubic shape. Also, arm is considered as a

rod of mass m, length ℓ, (so that m = ρ*ℓ*s), this rod is rotating

around the axis which passes through its center and is

perpendicular to the rod .The total equivalent inertia, Jequiv and

total equivalent damping, bequiv at the armature of the motor

with gears attaches, can be calculated from known formulae.

Input units Control unit Output unit

Sensors Converters Microcontroller Motor driver

Fig. 1. (a) Motion control system and components

Fig. 1. (b) motion control using microcontroller, and corresponding

feedback element.



Controller

(angle, speed)Control voltage,

Vc

Angle or Speed measure e,.g

Potentiometer, Tachometer

Sensor

+-

Error, VoltAngle or Speed

reference (desired)

Volt

Motor shaft

ω or θ

Fig. 1. (c)Two Block diagram representations of PMDC motor control

Error Angle or speed

Vpot or Vtach

Robot.mat

To File

Reference input

Output shft

angle, speed

-K-

Kpot or Ktach

In1 Out1

DC Motor

Subsystem

P(s)

Controller to be

selected and designed

Fig. 1. (d) Preliminary simulink model for negative feedback with

forward compensation

II.I ELECTRIC MOTOR MODELING

The actuators most used in mechatronics motion control

systems, are DC machines (motors). Because their torque-

speed characteristics are achievable with different electrical

configurations and their speeds can be smoothly controlled

and in most cases are reversible, also, DC Motor and its

features can be analyzed both by Control System design

calculation and by MATLAB software .There are many DC

motors that may be more or less appropriate to a specific type

of application each has its advantages, limitations and

disadvantages. The designer must select the best one fo r

specific application. In [11] different types of DC machines, are

introduced with their mathematical models, current and torque

characteristics, it was shown that allmostly, all DC machines

has identical models, therefore any DC machine can be used to

build the proposed motion model, to be accurate for each

particular case, it is required, only, to modify the used actuator

model. DC motors are an example of electromechanical

systems with electrical and mechanical components, it turns

electrical energy into mechanical energy and produces the

torque required to move the load to the desired output

position, θL, or rotate with the desired output angular speed,

ωL. The produced torque is exerted to accelerate the rotor and

ultimately this mechanical power will be transmitted through a

gear set to mechanical system part. The fundamental system of

electromagnetic equations for any electric motor is given by

[14-15]:

( )

ks

s s s s

kR

s R R b m R

s s s R

R R R S

du R i j

dt

du R i j P

dt

L i L i

L i L i

(1)

Where: k the angular speed of rotating coordinate system

(reference frame), Depending on motor construction (AC or

DC), the method of the supply and the coordinate system

(stationary or rotating with the rotor or stator flux) the above

mentioned model becomes transformed to the desirable form

[16]. To write the equivalent electric actuator model, for output

speed control, model of a symmetric half of the mobile robot

platform is constructed, the same model is used for output

angle control, as well as for current, torque and acceleration.

The PMDC motor open loop transfer functions without any

load attached relating the input voltage, Vin(s), to the motor

shaft output angle, θm(s), and speed ωm(s), are given by:

3 2

2

( )

( ) ( ) ( )

( )

( ) ( ) ( )

t

in a m a m m a a m t b

t

in a m a m m a a m t b

Ks

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

Ks

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

2

The transfer function of PMDC, equivalent to robot arm

transfer function, in terms of input volt and output angular

position, is given by:

3 2

( ) *

( ) ( ( )

arm t

in a equiv a equiv equiv a a equiv t b

s K n

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

3

The transfer function of PMDC, equivalent to mobile robot

platform transfer function, in terms of input volt and output

angular speed is given by:

2

( ) /

( ) ( ) ( ) ( )

mobile t

in a equiv a equiv equiv a a equiv t b

s K n

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

4

Major mechanical and electrical nonlinearities, (e.g. coulomb

friction), can be included, in this model, which is considered as

disturbance torque, and is given by:

Te – Tα – Tω - TEMF - Tf = 0

At steady is given by:

Tf = Te - b*ω

In the following calculation the disturbance torque, T, is all

torques including coulomb friction, and given by T=Tload+Tf ,

and correspondingly, the open-loop transfer function of the

PMDC, is given by:

2( )

( )

t

open

a a equiv equiv a a b t

KG s

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

5

The geometry of the part determines the moment of inertia (e.g.

cuboide, Cylindrical, rod, disc, sphere etc), equations for the

total equivalent inertia, Jequiv and total equivalent damping,

bequiv at the armature of the motor with gears attaches are given

in tables, for mobile robot the mobile platform can be



considered to be of the cuboid or cubic shape and calculated

by Eq.(6), also the total inertia can be calculated from the

energy conservation principle.

2

2 2

1 1

2 2

3

2 2

2

2

1

12 12

0.5* * 0.5* *

*

equiv m Load equiv m Load

mobile arm

total load

total

load

N Nb b b J J J

N N

bhJ J ml

m J

mJ

6

Considering that linear velocity of platform, depends on

motor's angular speed, wheels radius, r, and gear ratio, n,

substituting, gives:

2 2 2

2 2 2

* ,

* * *

*

shaft

total total

load

n rn

r n

m r m rJ

n n

Form robot arm application: The moment of inertia of the

robot arm can be found by computing the following integral:

2/2 3 3

/22

/2

/2

/ 8 12

3 3 12

ll

l

l

x m lx sdx s s ml

sl

Calculating and substituting values in (6) gives:

JLoad= (8*(0.4) ^2)/12 = 0.106666666666667 kg.m2

Substituting, we obtain, Jequiv ,to be :

Jequiv = Jm + Jload *(1/1)

Jequiv =0.02+0.107= 0.1267 kg·m²

Obtaining the total damping, b total , gives:

b equiv = bm + bload(1/1)

b equiv_arm = 0.03 + 0.09 = 0.12 N.sec/m

Form mobile robot application: The total equivalent inertia,

Jequiv and total equivalent damping, bequiv at the mobile robot

armature of the motor are ,Jequiv =0.2752 kg.m2 , bequiv = 0.3922

N.m.s. Neglecting the DC motor’s inductance, by assuming L

≈0, we have, transfer function relating input voltage and

output speed:

/( )

( ) 1

t a equiv

t b

equiv

equiv a

K R Js

V s K Ks b

J R

Transfer function relating input Vin (s) and output current:

1

( )

( ) 1

equiv

a equiv

t b

equiv

equiv a

bs

R JI s

V s K Ks b

J R

The transfer function relating the input voltage, Vin (s), to the

output armature current, Ia(s), directly follows:

2

1

( )

( )

a

a ma

in equiv a equiva b t

a equiv a m a equiv

Ls

L JI s

V s b R bR K Ks s

L J L J L J

Equation relating the torque developed by the motor and the

motor shaft angle is given by:

2

( ) 1

( )

m

m equiv equiv

s

T s J s b s

II.II SYSTEM DYNAMICS MODELING

When deriving an accurate mathematical model for motion

system it is important to study and analyze dynamics between

system and surroundings, and considering all the forces

applied upon the system. The suggested model will tested for

mechatronics motion control design applications of two

systems mobile robot and robot arm. For other systems the

proposed model will include a separate block for load torques

of particular application form and dimensions , such that the

model can be applied to any motion control system.

For robotic arm; Torque, T is defined as a turning or twisting

force and is calculated as given next: *T F L , Where: F The

force acts at a length, L, from a pivot point. The torque

required to hold a mass, m, at a given distance from a pivot is

therefore:

( * )*T m g L

To calculate the extra torque required to move (i.e. create an

angular acceleration), we calculate the moment of inertia of the

part from the end to the pivot. For mobile robotic platform; In

[4,13,17] an accurate derivation of all forces acting on mobile

platform system, when it is running are introduced. For mobile

robot, considering dimensions, and the following most acting

forces and corresponding torques, can be considered:

Rolling resistance force,

_ r rF C C cos( )R normal forceF Mg 7

In terms of the vehicle linear speed Eq.(7) becomes:

r0 r1F M *g * C -C * * ( )R sign

The rolling resistance torque is given by:

R rT * *C *cos( ) * wM g r 8

The hill-climbing resistance force is given by:

climbF * *sin( )M g 9

The hill-climbing resistance, slope, torque, is given by:

10 climb slopeT T = * *sin( ) * wheelM g r

The total inertia force of the mobile platform,

slopeF F =Minertia

d

dt

The inertia torque is given by:

2

slopeF F =r Minertia

d

dt

Aerodynamic Drag force, given by: 2

aerod dF 0.5 AC vehicl

The aerodynamics torque is given by:

2

aerod d

1T AC

2vehicle wr

The angular acceleration force is given by:



2

acc_ angle 2F

wheel

GJ

r 11

The angular acceleration torque is given by:

12 2 2

acc_ angle 2w

w w

G GT r J J

r r

III. CONTROLLER SELECTION AND DESIGN

The goal for a control system is to achieve a fast response to a

step command with minimal overshoot, and minimum error or

follow a given reference input signal [17]. The modern

advances in electric motors and controllers improve motors

speed, acceleration, controllability, and reliability; also allow

designers a wider choice of power and torque. The term

control system design refers to the process of selecting

feedback gains that meet design specifications in a closed-loop

control system. Most design methods are iterative, combining

parameter selection with analysis, simulation, and insight into

the dynamics of the plant [18]. There are many motor motion

control strategies that may be more or less appropriate to a

specific type of application each has its advantages and

disadvantages. The designer must select the best one for

specific application, in [11] most suitable control strategies for

DC motor motion control, are suggested, were different control

strategies were selected, designed, applied and their action

were compared to select the most suitable control of a given

DC motor in terms of output speed and angle, Most of these

suggested control strategies will be applied in suggested

system model, mainly PID, PI, PD as separate blocks to be

applied with and without deadbeat response, also lead and lag

compensators, the designer must select the best controller for

specific application.

Systems design with prefilter: Prefilter is defined as a transfer

function Gp(s) that filters the input signal R(s) prior to

calculating the error signal. Adding a control system to plant,

will result in the addition of poles and/or zeros, that will effect

the response, mainly the added zero, will significantly inversely

effect the response and should be cancelled by prefilter,

therefore the required prefilter transfer function to cancel the

zero is given by (13). In general. The prefilter is added for

systems with lead networks or PI compensators. A prefilter for

a system with a lag network, mainly, is not, since we expect the

effect of the zero to be insignificant.

Pr ( ) /efilter O OG s Z s Z 13

PID controller design: PID controllers are most used to

regulate and direct many different types of dynamic plants the

time-domain, The PID gains are to be designed and tuned to

obtain the desired overall desired response. The PID controller

transfer function is given by: 2

I D P I

PID P D

K K s K s KG K K

s s

14

Proportional Integral - PI controller is widely used in variable

speed applications and current regulation of electric motors,

because of its simplicity and ease of design. PI controller

transfer function is given by:

( )

( )

P II

PI P

I

P

P oP

PI

K s KKG s K

s s

KK s

K s ZKG s

s s

15

Where, Zo: Zero of the PI-controller, KP: The proportional gain.

The PI zero, Zo=- KI/ KP, will significantly and inversely effect

the response and should be cancelled by prefilter given by

(13).

Proportional -Derivative - PD controller: The transfer

function of PD-controller is given by Eq.(15) :

( ) ( ) ( )P

PD P D D D PD

D

KG s K K s K s K s Z

K 16

The PD-controller is equivalent to the addition of a simple

zero at: /PD P DZ K K

The required prefilter transfer function to cancel the PI- zero at

ZPI=KI/ KP is given by:

_ Pr ( ) /PI efilter PI PIG s Z s Z (17)

For systems with PD compensators, a prefilter is used to

eliminate any undesired effects of the term s + z introduced in

the closed-loop transfer function, the required prefilter transfer

function is given by:

_ Pr ( ) PD

PI efilter

PD

ZG s

s Z

Lead compensator: Lead compensator is a soft approximation

of PD-controller, the following approximated controller transfer

function of PD controller, and called lead compensator is given

by:

( ) Where : o

C o o

o

s ZG s K Z P

s P

18

If Z < P this controller is called a lead controller (or lead

compensator). If Z > P : this controller is called a lag controller

(or lag compensator) .

Lag compensator; The Lag compensator is a soft

approximation of PI controller, The Lag compensator transfer

function is given by.

19 ( )

( )

o

lag c

o

s ZG s K

s P

Where: Zo > Po, and Zo small numbers near zero and Zo =KI/KP

, the lag compensator zero. Po: small number ,The smaller we

make Po, the better this controller approximates the PI

controller.

Lead integral compensator controller transfer function is given

by:

_

( ) ( )1( )

( ) ( )

o oLead Integral C C

o o

s Z s ZG s K K

s s P s s P



Eliminating the steady state error, but disturb transient

response settling time, and overshoot.

III.I POSITION AND VELOCITY FEEDBACK SENSORS

MODELING; POTENTIOMETER AND TACHOMETER

To calculate the error, we need to convert the actual output

(position, speed, torque, current) into voltage, V, then compare

this voltage with the input voltage Vin, the difference is the

error signal in volts.

Potentiometer is a sensor used to measure the actual output

robot position, θL ,convert into corresponding volt, Vp and

then feeding back this value to controller, the Potentiometer

output is proportional to the actual position, θ L, this can be

accomplished as follows: The output voltage of potentiometer

is given by:

Vp = θL * Kpot

Where: θL :The actual position. Kpot the potentiometer

constant; It is equal to the ratio of the voltage change to the

corresponding angle change, and given

by: potK (Voltage change) / (Degree change) . Depending on

maximum desired output arm angle, the potentiometer can be

chosen. for our case, input volt range Vin= 0:12, and input

angle range θ= 0:180 degrees, substituting, we have:

12 0 / 180 0 0.0667 V / degreepotK

Potentiometer constant Kpot = 0.0667 V/degree. This value

(0.0667), means that each one input volt corresponds to

180/12= 15 output angle in radians , to obtain a desired output

angular position of 180 , we need to apply 12 volts, to obtain

an angular position of 90 we need to apply

( 90*0.0667= 6.0030 Volts).

Tachometer is a sensor used to measure the actual output

mobile robot angular speed, ωL .. Dynamics of tachometer can

be represented using the following equation:

* / *out tac out tacV t K d t dt V t K

The transfer function of the tachometer is given by:

Vout(s) / ω(s) =Ktac

A suitable linear output speed of domestic mobile robot is to

move with 0.5 m/s, that is:

V/r 0.5/0.075 6.6667 rad / s,

Tachometer constant, Ktac = 12 / 6.6667=1.8

III.II THE CONTROL OF OUTPUT POSITION (ROBOT

ARM) WITH POSITION AND VELOCITY FEEDBACK.

For the feedback system shown in Fig.2, a velocity feedback is

used to stabilize systems that tend to oscillate, for this system

the output is the angular displacement, θL, the rate of change of

angular position , dθL(s) /dt, is actual output angular speed,

and the error signal , Ve ,is given by:

* /e in pot o tac oV V K K d dt

Taking Laplace transform, and separating we have:

Ve(s) = Vin(s) - θL(s) *(Kpot - Ktac*s)

θL(s) = Ve (s)* Kcon *Garm(s)

Substituting, Ve, we have:

θL(s) = Ve (s)*Kcont* Garm(s)= K*G(s)[ Vin (s) - θL(s) *( Kpot -

Ktac *s)]

θL(s) = Kcont * Garm(s)*[ Vin (s) - θL(s) *( Kpot + Ktac *s)]

θL(s) = Kcont * Garm(s)* Vin (s) - Kcont * Garm(s)* θL(s) *( Kpot +

Ktac *s)

θL(s) + Kcont * Garm(s)* θL(s) *( Kpot + Ktac*s ) = Kcont *

Garm(s)* Vin (s)

θL(s) [ 1 + Kcont * Garm(s)*( Kpot + Ktac *s )] = Kcont * Garm(s)* Vin

(s)

The overall transfer function in terms of input voltage and

output angular position

con arm

arm

K *G ( )( )

( ) 1 *G ( ) *

L

in cont pot tac

ssTF

V s K s K K s

For this transfer function, if given the DC motor transfer

functions and parameters, controller transfer function and

sensors gains Kpot, Ktac, we can evaluate the behavior of our

system

Fig. 2. The control of output position with position and velocity

feedback.

IV. SYSTEM SIMULATIONS

In the proposed model the following sub-systems will be

simulated; electric actuator, input signals, most used and

proved control strategies for motion control, dynamics

between system and surroundings considering all the forces

applied upon the system. Based on derived equations, the

driving torques, can be simulated, with function block model as

shown in Fig. 3(a)(b) , also a repeating sequence stair model

can be used to simulate different disturbance torques. Different

inputs can be applied to the suggested model, to simulate

different real life inputs including; constant input, step, ramp,

motion reference profile, the simulation of motion profile is

shown in Fig. 3(d). PM Motor subsystem simulation is shown

in Fig. 4(a). The proposed model for mechatronics motion

control applications in terms of output speed and/or angle, as

well as torque, current, acceleration and controller action, is

shown in Fig. 4(b), While maintaining accuracy, this model will

simplify as well as accelerate Mechatronics systems design

process, both mechanical system and controller selection,

analysis, design and validation. This model can be used for



any mechatronics motion control application the use PM motor

as prime mover. The model allows designer, using manual

switches, to select each of the following; system to be deigned

and tested, (e.g. mobile robot, robot arm, conveyer ), select

control strategy ( PID, PI, PD, PI, with or without dead beat

response, lead or lag as well as lead integral compensator),

also, select input and disturbances type. The model, also,

allows visual readings of output speed, angle, as well as

torque, current, acceleration and controller action. It is

important to consider that this model can be modified to

include any control strategy, as well as, any DC machine,

depending on particular application, it is required, just to

modify, the used actuator model. The presented model allows

the use of MATLAB PID block, to be used as PI, PD and PID

controller with tuning capabilities, also a separate PD, PI

controllers models are included, as well as prefilter. Also, the

presented is support with MATLAB m.file to define and select

all system's parameters, dimensions and coefficients; that is

PMDC, mobile robot, robot arm, sensor, system dynamics and

controllers gains, poles and zeros, also this m.file can be used

separately to design, analyze derive and plot system's open

loop and closed loop transfer function in terms of output

speed and/or angle, as well as torque, current and acceleration.

r^2*m*g/2

1Load torqe

sin(u)

cos(u)

SinCos

Product4

Product2

Product13

Product1du/dt

Derivative1

-C-

g

0.5

5

Inclination angle

4

Angular speed

3 r, wheel radius

2m ,Load mass

1Rolling friction coefficient

Fig. 3. (a) Load torque simulation, considering and not considering

coulomb friction

r 2*m*g/2

Coloumb friction

1Load torqe

sin(u)

cos(u)

SinCos

Product4

Product3

Product2

Product13

Product1du/dt

Derivative1

-C-

g

0.5

7

bm

6

motor Torque, Kt*i

5

Inclination angle

4

Angular speed

3 r, wheel radius

2m ,Load mass

1

Rolling friction coefficient

Fig. 3. (b) Load torque simulation, considering and not considering

coulomb friction

Rolling f riction coef f icient

m ,Load mass

r, wheel radius

Angular speed

Inclination angle

Load torqe

Load Subsystem

Fig. 3. (c) Load torque function block model

1

Out1Switch1

Switch

Ramp

slope=2

Ramp

slope=1

12

Constant7.999

Clock

Fig. 3. (d) motion profile simulation.



Current

Torque

13 POSITION linear speed

12 mobile linear speed

11POSITION LINEAR Acceleration

10

OUTPUT from angle feedback

9

OUTPUT from speed feedback

8

controller singal

7

OUTPUT from summing to controller6

From input Volt to PI fi lter

5SPEED LINEAR Acceleration

4 Torque3 Curent

2 Angular position

1Angular speed

Sum.4

Sum.1

Product9

Product8Product7

Product5

Product4

Product3

Product2

Product13Product12

Product11

Product10

1

s

Integrator.2

1

s

Integrator..4

1

s

Integrator..1

du/dt .

du/dt ,1

du/dt ,

15 Wheel radius

14 sensor output13

Ktach, speed feedback

12n, Gear ratio11

From PI fi lter

10

Controller output

9

Kpot, angle feedback

8

bm

7

T, Load torque

6

Ra

5

Input Voltage

4Kt, Torque constant

3

Kb, EMF constant

2Jm

1La

Fig. 4. (a) Motor subsystem model.

IV.I MATLAB M.FILE

V.I.I SUPPORTING MATLAB PROGRAM

The model is support with, written below, MATLAB

m.file to define and select all system's parameters,

dimensions and coefficients, controller selection (PID, PI

with deadbeat, PD with deadbeat) analyze, derive and to plot

system's response output results in terms of speed and/or

angle, as well as torque, current and acceleration. Also this

m.file can be used separately to design, motion system and

controller selection (PID, PI with deadbeat, and PD with

deadbeat) analyze, derive and plot system's open loop and

closed loop transfer function and corresponding plots of

response curves:

clc, close all, clear all

format short

% First DC motor (used)parameters

% Vin=12 ; Kt= 1.1882 ; Ra = 0.1557; La

= 0.82; Jm = 0.271; bm=0.271; Kb =

1.185; Jm =0.271 ;n=1;

%Second DC motor (used) parameters

Vin=12 ;V=12; Kt= 0.023 ; Ra = 1; La =

0.23 ; Jm = 0.271; bm=0.03; Kb = 0.023;

n=1;Jm =0.02 ;n=1;

r=0.075;% m wheel radius

g=9.79379 ;% m/s^2, grav. acc.

mobile_robot_wedth=0.580 ;% m

mobile_robot_height=0.920 ;% m

desired_linear_speed=0.5;% m/s

desired_angular_speed=

(desired_linear_speed)/r;

m=100;% mobile total mass

b_mobile=0.09;rolling_f=0.01;Kp_PI=2;Kd_

PD=2;Zo=0.1;

Po=0.11;Kp_compensator=2;Tl=10;

Cr= 0.014; % Rolling Resistance

Coefficient

inclination_angle=45;

M= 8 ; Length=0.4 ; b_arm = 0.09 ;

angle_max=90;V_max =12;

Ktach =Vin/ desired_angular_speed;

Kpot=V_max /angle_max;

Kp_PI=2;Kd_PD=2;Zo=0.1;Po=0.2;

Kp_compensator=2;Tl=10;inclination_angle

=45;

Cr= 0.014; % Rolling Resistance Coe.

% Jm = input(' Enter Motor armature

moment of inertia (Jm) :');

% bm = input(' Enter damping constant

of the the motor system (bm):');

% Kb = input(' Enter ElectroMotive

Force constant (Kb):');

% Kt = input(' Enter Torque constant

(Kt):');

% Ra = input(' Enter electric

resistance of the motor armature (ohms),

(Ra):');

% La =input(' Enter electric

inductance of the motor armature

,Henry,(La) :');

% inclination_angle=input(' Enter

inclination angle :');

disp(' ')

disp( ' ==============================')

num1 = [1];

den1= [La ,Ra];

num2 = [1];

den2= [Jm ,bm];

A = conv( [La ,Ra], [Jm ,bm]);



TF1 =tf(Kt*n, A);

%obtaining open loop transfer functions

of DC motor system and step response

disp('DC motor OPEN loop transfer

function, Speed/Volt: ')

Gv= feedback(TF1,Kt)

disp( ' ==============================')

disp(' DC motor OPEN loop transfer

function, Angle/Volt: ')

Ga=tf(1,[1,0] )*Gv

subplot(2,1,1),step (V*Ga);title('

Position step response , open loop DC

motor system')

subplot(2,1,2),step (V*Gv);title(' Speed

step response , open loop DC motor

system')

disp( ' ==============================')

disp( ' DC motor response curves are

ploted')

disp( ' ==============================')

disp(' click any key to continue

');pause,home, disp(' ')

x=1;

while 1==1;

home

disp( ' ==============================')

disp(' It is required to design a

robot ARM or MOBILE robot? ')

disp( ' ==============================')

AA= input(' Enter (1) for Robot arm

design and enter (2) for Mobile robot

design: ','s');

disp( ' ==============================')

if strcmp(AA,'2')==1;

home, disp( ' ')

disp(' YOUR

choice is Mobile robot design ')

disp(' Please enter

robot dimensions and parameters :')

disp( ' ==============================')

disp(' click any key to continue

'); pause, home

% wheel_radius= input( ' Enter

mobile robot wheel radius : ' );

% mobile_robot_height= input( '

Enter mobile robot height : ' );

% mobile_robot_wedth= input(

' Enter mobile robot wedth : ' );

% Dist_wheels= input( '

Enter Disttance between wheels : ' );

% desired_linear_speed=

input( ' Enter mobile robot desired

output linear speed : ' );

% m= input( ' Enter mobile

robot total mass : ' );

% friction= input( ' Enter

rolling friction coefficient between the

wheel and road surface : ');

% V = input(' Enter

applied input voltage Vin :');

J_mobile =(mobile_robot_wedth*

(mobile_robot_height)^3)/12;

Jequiv_mobile = Jm+

J_mobile/(n)^2;

bequiv_mobile = bm +

b_mobile/(n)^2;

desired_angular_speed=

(desired_linear_speed)/r;

Ktach =Vin/

desired_angular_speed ;%tachometer

constant

num_mobile=[ Kt*n];

den_mobile=[La*Jequiv_mobile

,(Ra*Jequiv_mobile+bequiv_mobile*La),(Ra

* bequiv_mobile+Kt*Kb)];

disp( ' ==============================')

disp( ' mobile robot open loop transfer

function and step response')

disp( ' mobile robot open loop

transfer function, Omega/Volt')

G_robot_angular_speed_open=tf(num_mobile

, den_mobile)

disp( ' ==============================')


transfer function, linear speed/Volt')

G_robot_linear_speed_open=tf(num_mobile,

den_mobile)*r

disp( ' ==============================')


transfer function, Vin/Current')

G_robot_volt_current1=tf((1/Ra)*[1,

bequiv_mobile/Jequiv_mobile ],

[1,(1/Jequiv_mobile)*(bequiv_mobile+(Kt*

Kb)/Ra) ])

disp( ' ==============================')


function, Vin/Current')

G_robot_volt_current2=tf((1/La)*[1,

La/Jequiv_mobile ],

[1,(Ra/La)+(bequiv_mobile/Jequiv_mobile)

, (Ra*bequiv_mobile/La*Jequiv_mobile+

Kt*Kb/La*Jequiv_mobile) ])

disp( ' ==============================')




function, Torque/Angle')

G_robot_torque_angle=tf([1 ],

[(Jequiv_mobile)^2, bequiv_mobile,0

])

disp( ' ==============================')

disp( ' mobile robot CLOSED loop

transfer function, Linear speed/Vin')

G_robot_linear_speed_closed=feedback(G_r

obot_linear_speed_open, Ktach)

disp( ' ==============================')


transfer function, Vin/Vtach')

G_robot_linear_Vin_V_tach=tf([2*Kt*Ktach

],[r^2*m+2*bequiv_mobile,(Ra*(r^2*m+2*be

quiv_mobile))+La*(rolling_f

+2*Jequiv_mobile),Ra*(rolling_f

+2*Jequiv_mobile)+2*Kb*Kt ])

disp( ' ==============================')


transfer function, Linear speed/Vin')

G_robot_linear_speed_closed=feedback(G_r

obot_linear_Vin_V_tach,Ktach)

fig., subplot(3,2,1),

step(G_robot_angular_speed_open),ylabel(

'Mobile Angular speed, \omega Rad/s

'),xlabel(' Time '), title('Open loop

Mobile Angular speed Rad/s, '), grid,

subplot(3,2,2),step(G_robot_linear_speed

_open),ylabel('Mobile linear speed, \nu

Rad/s '),xlabel(' Time '), title('Open

loopMobile linear speed m/s, '), grid,


_closed),ylabel('Mobile linear speed,

\nu Rad/s '),xlabel(' Time '),

title('Closed loop Mobile linear speed

m/s, '), grid,

subplot(3,2,4),step(G_robot_volt_current

1),ylabel('Mobile current Amp

'),xlabel(' Time '), title('simplified

Input volt vs current, '), grid

subplot(3,2,5),step(G_robot_volt_current

2),ylabel('Mobile current Amp

'),xlabel(' Time '), title(' Input volt

vs current, '), grid

subplot(3,2,6),step(G_robot_torque_angle

),ylabel('Mobile torque '),xlabel(' Time

'), title(' Input torque vs angle, '),

grid, fig.

subplot(2,1,1),step(G_robot_linear_Vin_V

_tach),ylabel('Mobile Vin vs Vtach


vs tacho output volt, '), grid


_closed),ylabel('Mobile speed


vs output speed, '), grid

pause(2); home

disp( ' ==============================')

disp( ' select controller; PID or PI

with dead beat response? ')

WW= input( ' Enter (1) for PID, enter

(2) for PI with deadbeat response:

','s');

disp( ' ==============================')

if strcmp(WW,'1')==1;

home, disp( ' '); disp( '

==============================')

disp(' YOUR choice is PID controller

for mobile robot control ')

disp(' Enter PID gains : ')

disp(' you can run simulink model and

use gain from PID block : ')

disp( ' ==============================')

Kp= input( ' Enter Proportional gain, Kp

= ');Kd= input( ' Enter Derivative

gain, Kd = ');Ki= input( ' Enter

Integral gain, Ki = ');PID_num=[ Kd Kp

Ki];PID_den=[ 1 0];

disp( ' ==============================')

disp( ' PID transfer function')

G_PID=tf(PID_num,PID_den)

G_forward_PID=

series(G_PID,G_robot_linear_Vin_V_tach);

disp( ' ==============================')

disp( ' mobile robot closed loop with

PID transfer function, /linear

speed/Vin')

G_mobile_PID_closed=

feedback(G_forward_PID, Ktach);fig.

step(G_mobile_PID_closed),ylabel('Mobile

Vin vs Vtach '),xlabel(' Time '),

title(' Input volt vs tacho output volt,

'), grid;

step(G_robot_linear_speed_closed),ylabel

('Mobile speed '),xlabel(' Time '),

title(' Input volt vs output speed, '),

grid

else strcmp(WW,'2')=1;

home; disp( ' ')

disp( ' ==============================')

disp(' YOUR choice is PI controller with

deadbeat response for mobile robot

control ')

disp( ' ==============================')

alpha=1.9;bita=2.2;Ts=1.2;omega_n=4.04/T

s;

Kp=((bita*(omega_n^2)*n*La*Jequiv_mobile

)-

((n*Ra*bequiv_mobile)+(n*Kt*Kb)))/(Kt*Kt

ach); Kp_PI=Kp;

Ki=omega_n^3*n*La*Jequiv_mobile/(Ktach*K

t); ZPI= Ki/Kp; Home, disp(' ')

disp( ' ==============================')



disp( ' PI controller & Deadbeat

prefilter gains and zero are :')

fprintf(' Kp_PI =%g , Ki=%g

,ZPI=%g \n',Kp,Ki,ZPI);

num_deadbeat=[Ki*Kt/(n*La*Jequiv_mobile)

]; den_deadbeat=[1 , (Ra*Jequiv_mobile

+bequiv_mobile*La)/(La*Jequiv_mobile) ,

((n*Ra*bequiv_mobile)+(n*Kt*Kb)+(Ktach*K

p*Kt))/(n*La*Jequiv_mobile) ,

(Ktach*Ki*Kt)/(n*La*Jequiv_mobile)];

disp( ' ==============================')

disp('Closed loop transfer function with

PI deadbeat respnse & prefilter ')

T_mobile_deadbeat

=tf(num_deadbeat,den_deadbeat)

;fig., step(12*r*T_mobile_deadbeat);

ylabel('Mobile linear speed \nu

'),xlabel(' Time '), title('Mobile

linear, PI with Dead beat response, '),

grid,

end

else strcmp(AA,'1')==1;home

disp( ' ')

disp( ' ==============================')

disp(' YOUR choice is

Robot arm design ')

disp(' Please enter Arm

dimensions and parameters :')

disp( ' ==============================')

% M= input(' Enter robot

arm mass , M=');

% Length = input(' Enter

robot arm Length, L=');

% b_arm= input(' Enter damping

factor of robot arm, b_arm =');

% n= input( 'Enter gear

ratio n = ');

% V = input(' Enter

applied input voltage Vin :');

% V_max = input(' Enter

maximum allowed voltage , V max :');

% Angle_max = input( ' Enter maximum

allowed angle for robot arm : ');

Kpot=V_max /angle_max; % pot

constsnt

Jequiv=((M* Length^2)/12)+Jm;

bequiv= bm + b_arm;

num_arm_open = [Kt*n*(180/pi)];

den_arm_open=[La*Jequiv

(Ra*Jequiv+La*bequiv)

(Ra*bequiv+Kt*Kb) 0];

disp(' ');

disp(' click any key to continue ');

pause; home; disp( '

==============================')

disp('Arm OPEN loop transfer function :

')

Ga_arm_open=tf(num_arm_open,den_arm_open

)

disp( ' ==============================')

disp('Arm CLOSED loop transfer function

: ');

G_close_arm=feedback(Ga_arm_open,(Kpot/n

)); disp( ' Response plots are plotted

'); fig.; subplot(2,1,1),

step(V*Ga_arm_open);ylabel('Arm

position, \theta Rad '),xlabel(' Time

'), title('OPEN loop Arm Angular

position Rad/s, '), grid;

subplot(2,1,2),step(V*G_close_arm);ylabe

l('Arm position, \theta Rad

'),xlabel(' Time '), title('CLOSED loop

Arm Angular position Rad/s, '), grid,

home; disp( '

==============================')

disp( ' select controller; PID, PD with

dead beat response? ')

WWW= input( ' Enter (1) for PID, enter

(2) for PD with deadbeat response:

','s');

disp( ' ==============================')

if strcmp(WWW,'1')

home, disp( ' ')

disp( ' ==============================')

disp(' YOUR choice is PID

controller for robot arm ')

disp(' Enter PID gains : ')

disp(' you can run simulink

model and use gain from PID block : ')

disp( ' ==============================')

Kp= input( ' Enter Proportional gain,

Kp = ');

Kd= input( ' Enter Derivative gain, Kd =

');

Ki= input( ' Enter Integral gain, Ki =

');

PID_num=[ Kd Kp Ki];PID_den=[ 1 0];

Home, disp( ' ')

disp( ' ==============================')

disp( ' PID transfer function')

G_PID=tf(PID_num,PID_den)

disp( ' ==============================')

disp( ' Closed loop Robot arm transfer

function with PID')

G_forward_PID=

series(G_PID,Ga_arm_open);

G_arm_PID_closed=

feedback(G_forward_PID, Kpot)

fig.

step(V*G_arm_PID_closed),ylabel('Arm

angle \theta Rad '),xlabel(' Time '),



title(' Input volt vs output

Armangle,PID '), grid

else strcmp(WWW,'2')==1;

home, disp( ' ')

disp( ' ==============================')

disp(' YOUR choice is robot arm design

; PD controller with dead bead

controller response ')

disp( ' ==============================')

omega_n=2.4;alpha=1.82 ;

disp( ' PD transfer function = Kds + Kp

is given by :')

Kp=(omega_n*Ra*Jm)/(Kt*Jequiv);

Kp_PD=Kp;Kd=(((alpha*omega_n)-(bm/Jm)-

((Kt*Kb)/(Jequiv*Ra)))*Ra*Jequiv)/Kt*Kpo

t;ZPD=Kp/Kd;ZPI=ZPD;G_PD=Kd*[ 1 ZPD];

num_arm_PD =G_PD* [Kt*n];

den_arm_PD=[La*Jequiv

(Ra*Jequiv+La*bequiv)

(Ra*bequiv+Kt*Kb) 0];

G_mobile_PD_tf= tf(num_arm_PD,

den_arm_PD);G_mobile_PD_dead_closed=

feedback(G_mobile_PD_tf, Kpot);

disp(' ')

disp( ' ==============================')

disp( ' PD controller & Deadbeat

prefilter gains and zero are :')

fprintf(' Kp_PI =%g , Kd=%g ,ZPd=%g

\n',Kp,Kd,ZPd);

disp( ' ==============================')

disp( ' Prefilter transfer function :');

prefilter_num=[ZPD];prefilter_den=[1

ZPD];G_prefilter=tf(prefilter_num,prefil

ter_den)

disp( ' ==============================')

disp( ' Robot arm overall closed loop

transfer function :')

G_mobile_PD_dead_overall=series(G_prefil

ter,G_mobile_PD_dead_closed)

Fig.,

step(V*G_mobile_PD_dead_overall),ylabel(

'Mobile speed \nu'),xlabel(' Time '),

title(' Arm PD with deadbeat response,

'), grid

disp(' click any key to continue ');

pause, end, end, end,

x=x+1; end

IV.I.II MATLAB CODE FOR PLOTTING ALL

SIMULATION RESPONSE CURVES

By defining blocks in simulink model, running simulation, all

data will de defined in MATLAB workspace , To plot all

response curves, run simulation then the next code, can be

used:

load model1.mat ,load model2 ,load

model3 ,load model4 ,load model5,load

model6,load model7,load model8,load

model9,load model10,load model11;fig.,

subplot(2,2,1);plot(model_angular_positi

on), ylabel('\Theta , Rad'),xlabel('

'), title('Angular position Rad '), grid

subplot(2,2,2);plot(model_angular_speed)

, ylabel('Angular speed, \omega Rad/s

'),xlabel(' '), title('Angular speed

Rad/Time, '), grid; subplot(2,2,4);

plot(model_angular_speed_RPM),

ylabel('Angular speed, RPM

'),xlabel('Time(sec)'), title('Angular

speed RPM, '), grid;

subplot(2,2,3);plot(model_current),

ylabel('Current, Amp

'),xlabel('Time(sec)'), title('Current

Amp/s, '), grid; fig., subplot(2,2,1);

plot(model_Torque), ylabel('Motor

Torque, Nm'),xlabel(' '), title('Motor

Torque Nm/Time '), grid; subplot(2,2,2);

plot(load_torque), ylabel('Load Torque,

Nm'),xlabel(' '), title('Load Torque

Nm/Time '), grid

subplot(2,2,3);plot(model_linear_acceler

ation), ylabel('Linear speed Accel.,

M/s^2'),xlabel('Time(sec)'),

title('Acceleration of Linear speed

M/Time '), grid; subplot(2,2,4);

plot(model_position_linear_acceleration)

, ylabel(' Position Accel.,

M/s^2'),xlabel('Time(sec)'),

title('Acceleration of Position /Time

'), grid, fig., subplot(2,2,1);

plot(model_linear_speed), ylabel('

Mobile linear speed.,

M/s'),xlabel('Time(sec)'), title('mobile

linear speed M/s '),

grid;subplot(2,2,2);plot(model_angel_lin

ear_speed), ylabel(' Angle linear

speed., M/s'),xlabel(' Time(sec) '),

title('Angle linear speed M/s '), grid

subplot(2,2,3); plot(controller_action),

ylabel(' controller_action'),

xlabel('Time(sec)'), title('controller

signal (mA)'), grid

V. TESTING AND ANALYSIS

VI.I Mechatronics motion control design in terms of output

linear speed of Mobile robot; plant, components, controller

selection, design and evaluation of output speed, current,

torque and acceleration and angle.

It is required to select, design and integrate a Mobile robot

system, with suitable selection of it's corresponding

mechanical parts, actuator's and sensor's parameters and



platform dimensions, to move with linear speed of 0.5 m/s,

(that is with angular speed of ω=V/r = 0.5/ 0.075 = 6.6667

Rad./s,), , here notice that, when defining system

parameters, using m.file, designer can chose and define

tachometer constant Ktach, corresponding to desired output

linear speed.

Now, switching the proposed model to output speed control

(mobile robot, conveyer belts, rolling) ,by switching sensor

to read output speed, selecting input signal to be step input

of 12 volts, selecting PID controller, running supporting

m.file to define system parameters, dimensions and

constrains, and finally running simulation, will result in

output speed, current, torque, acceleration and angle

response curves shown in Fig. 5, also direct visual readings

of all final outputs values can be taken, directly, from the

general model, the simulation results shows that the mobile

robot system, with selected parameters, dimensions and

applying PID controller with suitable gains, reaches, the

desired output linear speed of 0.5 m/s, in 0.35s, and zero

steady state error, constant current consumption, the PID

gains are KP=303.417042667051, KI= 414.72923375291,

KD=18.789820346901 . Now, to test designed system

robustness, Keeping the same parameters, but switching the

input to profile input signal and applying stair changing

disturbance, will result in response curves shown in Fig. 6,

the response curve show that system, while achieving

design criteria, maintain design criteria under disturbance

effect.

Now, to test and analyze the effect of applying Lead

integral compensator, we replace the PID controller, with

Lead integral compensator with Zo=.1; Kp =0.4; Po=0.091;

Ruining the model, will result in response curves shown in

Fig. 7, the gain , pole and zero can be adjusted for better

response.

Now, to test and analyze the effect of applying PI controller

with deadbeat response, we replace the PID controller with,

PI with deadbeat response, by switching the system to PI

controller and switching-on the prefilter, the PI zero, Zo= KI/

KP, can be defined from either supporting m.file calculations

results or using modified PID block to simulate PI and

tuning. Ruining the model, will result in response curves

shown in Fig. 8.

Using the resulted response curves and/or visual readings

from model, we can evaluate and/or validate our selection

and design and correspondingly we can or adjust or select

most suitable controller or change system parameters to

meet design criteria. In conclusion the design, modeling,

simulation and evaluation processes of motion control are

minimized in time, and also simplified.

VI.II Mechatronics motion control design in terms of output

angular displacement of a robot arm: plant and controller

selection, design and evaluation of output angle, current,

torque and acceleration and speed.

It is required to select, design and integrate a single joint

robot arm system, with suitable selection of it's mechanical

part, actuator, sensor parameters and dimensions , so that an

input voltage in the range of 0 to 12 volts corresponds

linearly of Robot arm output angle range of 0 to 180, that is

to move the robot arm to the desired output angular

position, θL , corresponding to the applied input voltage ,Vin

, Kpot =(12/180=0.0667), Switching the proposed general

model to output angle control (robot arm), by switching

sensor to read output angular displacement, s witching load

torque ,selecting input signal to step input of 12 volts,

selecting PID controller, running supporting m.file to define

system parameters, constrains and parameters, and finally

running simulation, will result in output angular

displacement, current, torque, acceleration and angle

response curves shown in Fig. 9 . Now, changing the

desired output angle output range to 0 to 45. ( for θ = 45,

Kpot =12/45=0.2667), Ruining the model, will result in

response curves shown in Fig. 10. Using the resulted

response curves and/or visual readings from model, we can

evaluate or validate our selection, design and

correspondingly we can or adjust or replace controller or

change system parameters to meet design criteria.

The proposed general model can be used to test, evaluate

and validate any given mechatronics motion control system

design e.g. electric cars, locomotives, turbines, robotics,

conveyer belts, rolling, cutting, welding, saws and bending

machines.

0 0.5 1 1.5-0.2

0

0.2

0.4

0.6

Time(sec)

Mobile

lin

ear

speed.,

M/s

mobile linear speed M/s

0 0.5 1 1.5-0.2

0

0.2

0.4

0.6

Time(sec) A

ngle

lin

ear

speed.,

M/s

Angle linear speed M/s

Fig. 5. (a) mobile robot output linear speed, and angle change vs time

responses

0 0.5 1 1.5-5

0

5

10

,

Rad

Angular position Rad

0 0.5 1 1.5-5

0

5

10

Angula

r speed,

Rad/s

Angular speed Rad/Time,

0 0.5 1 1.5-50

0

50

100

Time(sec)

Angula

r speed,

RP

M

Angular speed RPM,

0 0.5 1 1.50

100

200

300

Time(sec)

Curr

ent,

A

mp

Current Amp/s,

Fig. 5. (b) mobile robot output angular position, angular speed,

current vs time responses



0 0.5 1 1.50

100

200

300

Moto

r T

orq

ue,

Nm

Motor Torque Nm/Time

0 0.5 1 1.5-100

0

100

200

Load T

orq

ue,

Nm

Load Torque Nm/Time

0 0.5 1 1.5-10

0

10

20

30

Time(sec)

Lin

ear

speed A

ccel.,

M/s

2

Acceleration of Linear speed M/Time

0 0.5 1 1.5-0.2

0

0.2

0.4

0.6

Time(sec)

Positio

n A

ccel.,

M/s

2

Acceleration of Position /Time

Fig. 5. (c) mobile robot output motor torque, load torque, linear

acceleration and acceleration vs time responses.

0 2 4 6-0.2

0

0.2

0.4

0.6

Time(sec)

Mobile

lin

ear

speed.,

M/s


0 2 4 6 8-1

-0.5

0

0.5

1

Time(sec)

Angle

lin

ear

speed.,

M/s


Fig. 6. (b) mobile robot output linear speed, and angle change vs time

responses applying motion profile input .

0 2 4 6-10

0

10

20

30

,

Rad


0 2 4 6-5

0

5

10

Angula

r speed,

Rad/s


0 2 4 6-50

0

50

100

Time(sec)

Angula

r speed,

RP

M

Angular speed RPM,

0 2 4 60

50

100

150

Time(sec)

Curr

ent,

A

mp

Current Amp/s,

Fig. 6. (b) mobile robot output angular position, angular speed and

current response curves applying motion profile. input

0 5 10 15 20-0.2

0

0.2

0.4

0.6

Time(sec)

Mobile

lin

ear

speed.,

M/s


0 5 10 15 20-0.2

0

0.2

0.4

0.6

Time(sec)

Angle

lin

ear

speed.,

M/s


0 5 10 15 200

5

10

15

Time(sec)

contr

olle

r action

controller signal (mA)

Fig. 7. Mobile robot; linear speed vs time response applying Lead

integral compensator

0 2 4 6-0.2

0

0.2

0.4

0.6

Time(sec)

Mobile

lin

ear

speed.,

M/s


0 2 4 6-0.2

0

0.2

0.4

0.6

Time(sec)

Angle

lin

ear

speed.,

M/s


0 2 4 6-500

0

500

1000

Time(sec)

contr

olle

r action


Fig. 8. Mobile robot output linear speed vs time response of applying

PI with deadbeat response.

0 5 100

50

100

150

200

,

Rad


0 5 10-50

0

50

100

Time(sec)

Angula

r speed,

Rad/s


0 5 10-1

0

1

2

3

Time(sec)

Moto

r T

orq

ue,

Nm

Motor Torque Nm/Time

0 5 10-5

0

5

10

Time(sec)

Angle

lin

ear

speed.,

M/s


Fig. 9. (a) Robot arm response; output position, torque, speed vs

time response curves

0 5 10-2

0

2

4

6

Time(sec)

Positio

n A

ccel.,

M/s

2

Acceleration of Position /Time

0 5 10-50

0

50

100

Time(sec)

Curr

ent,

A

mp

Current Amp/s,

0 5 10-5

0

5

10

15x 10

4

Time(sec)

contr

olle

r action


0 5 10-500

0

500

1000

Time(sec)

Angula

r speed,

RP

M

Angular speed RPM,

Fig. 9. (b) Robot arm response ; acceleration, current and speed vs

time response curves

0 1 2 3 4-20

0

20

40

60

Time (seconds)

Angle

Output Angle

0 1 2 3 4-50

0

50

100

150

Time (seconds)

om

ega

Output speed

0 1 2 3 4-1000

0

1000

2000

.

Am

plit

ude

Torque

0 1 2 3 4-50

0

50

100

150

.

Am

plit

ude

Current

Fig. 10. Robot arm output position and Speed vs time response curves

for desired output of 45, Kpot =0.2667



PI C

ontro

ller

Lead

integ

ral co

mp.

PD-C

ontro

ller

spee

d sen

sor

Load

torqu

e

REFE

RENC

E IN

PUT

( SPP

ED or

ANG

LE)

agle

sens

or

Kt*i

r

whee

l radiu

s

spee

d LIN

EAR

acce

lerati

on m

/m^2

spee

d LIN

EAR

acce

lerati

on

rr

Out1

profile

inpu

t_1

posit

ion lin

ear s

peed

m/s

n n

-C-

inclin

ation

_ang

le

contr

oller

signa

l

-K- _

Torqu

e in N

/m

Torqu

e

mode

l8.ma

t

To Fi

le5

mode

l7.ma

t

To Fi

le4

mode

l6.ma

t

To Fi

le3

Tl Tloa

d

Repe

ating

Sequ

ence

Stair

Ra Ra

Out1

Prfile

inpu

t_2

Posit

ion lin

ear s

peed

Posit

ion lin

ear a

ccele

ration

m/s

2

Posit

ion lin

ear a

ccele

ration

PID(

s)

PID

Contr

oller

Mobil

e line

ar sp

eed m

/s

Mobil

e line

ar sp

eed

Load

torqu

e.,

Load

torqu

e,.

Rollin

g fric

tion c

oeffi

cient

m ,Lo

ad m

ass

r, wh

eel ra

dius

Angu

lar sp

eed

Inclin

ation

angle

motor

Torqu

e, Kt

*i bm

Load

torqe Load

torqu

e Sub

system

Load

torqu

e

s+Zo

s+Po

Lead

or la

g

La La

Ktac

h

Ktac

h

Kt Kt

Kpot

Kpot

Kb Kb

Jm Jm

Input

Volt (

0:12)

9.55

-K- Ga

in

du/dt

Deriv

ative

ZPI

s+ZP

I

Dead

beat

PI-pr

efilte

r

ZPD

s+ZP

D

Dead

beat

PD-pr

efilte

r

Curre

nt.

Curre

nt in

Amp

Contr

oller

actio

n

bmBm.

bm Bm

Angu

lar sp

eed.

Angu

lar sp

eed i

n RPM

Angu

lar po

sition

. Angu

lar po

sition

in ra

d

ANGU

LAR

spee

d in r

ad/se

c

ANGU

LAR

spee

d in R

PM

La Jm Kb, E

MF co

nstan

t

Kt, T

orque

cons

tant

Input

Volta

ge

Ra T, Lo

ad to

rque

bm Kpot,

angle

feed

back

Contr

oller

outpu

t

From

PI f

ilter

n, Ge

ar rat

io

Ktac

h, sp

eed f

eedb

ack

sens

or ou

tput

Whe

el rad

ius

Angu

lar sp

eed

Angu

lar po

sition

Curen

t

Torqu

e

SPEE

D LIN

EAR

Acce

lerati

on

From

inpu

t Volt

to P

I filte

r

OUTP

UT fr

om su

mming

to co

ntroll

er

contr

oller

singa

l

OUTP

UT fr

om sp

eed f

eedb

ack

OUTP

UT fr

om an

gle fe

edba

ck

POSI

TION

LINE

AR A

ccele

ration

mobil

e line

ar sp

eed

POSI

TION

linea

r spe

ed

ACTU

ATOR

Sub

system

mode

l11.m

at

.2

mode

l10.m

at

.1

...

..,

-K- ..

Cr.-

.,.

-K- .,

mode

l1.ma

t

.

s+ZP

I

s -

mode

l4.ma

t

,.

0 ,,.1

36 ,,.mo

del5.

mat

,,

m,

1 s `

9

8

7

6

5

4

3

2

10

1

mode

l3.ma

t

.

mode

l9.ma

t

mode

l2.ma

t

Fig. 4. The general purpose model, for mechatronics motion control applications in terms of output speed and/or angle, as well as torque, current and

acceleration

VI. SCOPE AND LIMITATIONS

The proposed model with load torque models is limited to

motion control systems design, and tested particularly, for

mobile robotic platforms speed and single joint robotic arms

position using electric actuators as prime mover, but can,

also, be used for system and motions control design and

verification of any given system, considering system's load

torque and inertia. The proposed model can be modified to

include any control strategy and/or any actuator model

CONCLUSION

To help in facing the two top challenges faced in developing

mechatronic systems, while maintaining desired accuracy

and to optimize system level performance to meet the design

requirements, an accurate mathematical and simulink models

are proposed for accurate mechatronics design and

verification of both system and control of motions

throughout Mechatronics systems design and development

process, including proper selection, analysis, integration

and verification of the overall system and sub-systems

performance in terms of output speed, angle, torque, current,

acceleration and signals , resulting in simplifying and

accelerating Mechatronics systems design process. The

proposed models intended to be used for research purposes

in mechatronics motion systems design, motion control

applications, as well as, for the application in educational

process. The proposed model can be modified to include

any control strategy and/or any actuator. The model was

created and verified using MATLAB simulink software.

The proposed model can be used to select most suitable

control strategy (P, PI, PD, PID, lead, lag, lead integral and

deadbeat response) for corresponding motion control and

to ensure achieving all design requirements , also test,

evaluate and validate any given mechatronics motion



control system design including; electric cars, locomotives,

turbines, robotics, conveyer belts, rolling, cutting, welding,

saws and bending machines, where designer using the

resulted, from model, response curves and/or visual

numerical readings, can early identifying system level

problems and ensuring that all design requirements are met ,

therefore the design, modeling, simulation and verifying

processes of motion control are minimized in time and also

simplified.

REFERENCES [1] Wilfried Voss, ''A Comprehensible Guide to Servo Motor Sizing'',

Published by Copperhill Technologies Corporation,

Massachusetts, 2007.

[2] Devdas Shetty, Richard A. Kolk, Mechatronics System Design,

Second Edition, SI, Cengage Learning, 2011.

[3] K. Craig, F. Stolfi, “ Teaching control system design through

mechatronics: academic and industrial perspectives.”

Mechatronics, Vol 12, No. 2, pp. 371-381, 2002.

[4] Vasilije S. Vasić , Mihailo P. Lazarević, Standard Industrial

Guideline for Mechatronic Product Design , FME Transactions,

104 , vol. 36, No 3, 2008.

[5] Grzegorz Seiklucki,Analysis of the Transfer-Function Models of

Electric Drives with Controlled Voltage Source PRZEGL ˛ AD

ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-

2097, R.88NR7a/2012

[6] Yu Wang, Ying Yu,Chun Xie, Xiaoyang Zhang, Weizhi Jiang, A

proposed approach to mechatronics design education:

Integrating design methodology, simulation with projects,

Mechatronics, November 2012.

[7] 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, 2013, 05, 39-57.

[8] 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

[9] Farhan A. Salem ; Mechatronics design of general and accurate

model for Mechatronics mobile robotic platform system and

controller, selection, design, modeling, testing and validation.

Submitted and under review to Estonian Journal of Engineering,

2013

[10] Bashir M. Y. Nouri ,modeling and control of mobile robots

Proceeding of the First International Conference on Modeling,

Simulation and Applied Opt imization, Sharjah, U.A.E. February

1-3, 2005.

[11] Farhan A. Salem Ahmad A. Mahfouz, Modeling, controller

selection and design of electric motor for mechatronics motion

applications, using different control strategies and verification

using MATLAB/Simulink (II). Submitted and accepted, , 2012

[12] Ahmad A. Mahfouz, Ayman A. Aly, Farhan A.

Salem,"Mechatronics Design of a Mobile Robot System", IJISA,

vol.5, no.3, pp.23-36, 2013.

[13] Farhan A. Salem, Mechatronics design of Small electric Vehicle's

,International Journal of Mechanical & Mechatronics

Engineering 1310701-5252 IJMME / IJENS

[14] M.P.Kazmierkowski, H.Tunia "Automatic Control of

Converter-Fed Drives", Warszawa 1994.

[15] R.D. Doncker, D.W.J. Pulle, and A. Veltman. Advanced Electri-

cal Drives: Analysis, Modeling, Control. Springer, 2011.

[16] Farhan A. Salem, Mechatronics motion control design of

electric motor for desired deadbeat response specifications,

supported and verified by new MATLAB built -in function and

simulink model, Submitted to Int. J. Intelligent Systems

Technologies and Applications, 2012

[17] Hedaya Alasooly, Control of DC motor using different control

strategies, global journal of technology and optimization, volum

2 , 2011.

[18] MathWorks, 2001, Introduction to MATLAB, the MathWorks,

Inc. Control System Toolbox, the MathWorks, Inc.

[19] Richard C. Dorf, Robert H. Bishop, Modern Control Systems 12

Ed, Pearson Education, Inc., 2001

[20] Thomas R. Kurfess, “Robotic and Automation Handbook,”

Washington, D.C., United States of Amarica, 2005.

[21] M.P.Kazmierkowski, H.Tunia "Automatic Control of

Converter-Fed Drives", Warszawa 1994.

NAMENCLATURE

Symbol Quantity UNIT

Vin The applied input voltage Volte, V

Ra Armature resistance Ohm ,Ω

ia Armature current Ampere, A

Kt Motor torque constant N.m/A

Ke Motor back-electromotive force. V/(rad/s)

ωm Motor shaft angular velocity rad/s

Tm Torque produced by the motor N.m

Jm Motor armature moment of inertia kg.m2

Jtotal Total inertia=Jm+Jload kg.m2

La Armature inductance Henry , H

b Viscousdamping friction coefficient N.m/rad.s

ea ,EMF: The back electromotive force, ea ,EMF:

θm Motor shaft output angular

position

radians

ωm Motor shaft output angular speed rad/sec

M The mass of the platform and

cargo

Kg

g The gravity acceleration m/s2

α Road or the hill climbing angle,

road slope

Rad

Cr The rolling resistance coefficients

Cd Aerodynamic drag coefficient

Zo Zero of the PI-controller

Tf coulomb friction torque

KP The proportional gain,:

KI The Integral gain

KD The derivative gain

KPI The proportional coefficient

Kpot The potentiometer constant



Ktac The tachometer constant

Farhan Atallah Salem AbuMahfouz :

B.Sc., M.Sc and Ph.D., in Mechatronics of

production systems. Now he is ass. professor

in Taif University, Mechatronics sec., Dept.

of Mechanical Engineering and director of

alpha center for engineering studies and

technology researches. Research Interests;

Design, modeling and analysis of primary

Mechatronics Machines. Control and algorithm selection, design and

analysis for Mechatronics systems. Rotor Dynamics and Design for

Mechatronics applications

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Mechatronics Design of Motion Systems; Modeling, Control ... · PDF fileMechatronics Design of Motion Systems; Modeling, Control and Verification. Farhan A. Salem1,2 1Mechatronics