Application of CI in Motor Modeling

International Journal of Computer Applications (0975 – 8887)
Volume 35– No.12, December 2011

Application of Computational Intelligence in
Motor Modeling

Yousuf Ibrahim Khan, Shahriar Rahman, Debasis Baishnab,
Mohammed Moaz, S.M. Musfequr Rahman
Department of Electrical and Electronic Engineering,
American International University-Bangladesh

ABSTRACT of equations that describe the underlying physical properties
Modeling is very important in the field of science and [2]. Not only do modeling and simulation help provide a
engineering. Modeling gives us an abstract and mathematical better understanding of how real-world systems function, they
description of a particular system and describes its behavior. also enable us to predict system behavior before a system is
Once we get the model of a system then we can work with actually built and analyze systems accurately under varying
that in various applications without using the original system operating conditions. Modeling is an integral part of Control
repeatedly. Computational Intelligence method like Artificial Systems and Motor drives. If we can find the model of a
Neural Network is very sophisticated tool for modeling and motor and give it a portability and hardware realization then
data fitting problems. Modeling of Electrical motors can also different experiments can be done with that model without
be done using ANN. The Neural network that will represent even accessing the motor repeatedly. It will show how that
the model of the motor will be a useful tool for future use particular motor will act in different applications and control
especially in digital control systems. The parallel structure of systems. Computational Intelligence techniques like Artificial
a neural network makes it potentially fast for the computation Neural Networks can be used to build such models and can
of certain tasks. The same feature makes a neural network give us chance to use the motor behavior in various analog-
well suited for implementation in VLSI technology. Hardware digital mixed signal applications where integrated circuits
realization of a Neural Network (NN), to a large extent play vital role (ASIC, FPGA, SoC). Hardware realization of
depends on the efficient implementation of a single neuron. In neural networks are possible [3]. FPGA-based reconfigurable
this paper only a motor model is presented along with some computing architectures are suitable for hardware
neural networks those will mimic the motor behavior implementation of neural networks. FPGA realization of
acquiring data from the original motor output. ANNs with a large number of neurons is still a challenging
task but will be possible very soon. Then researchers will be
able to work with those models. It will be like an entire
General Terms original control system or controller on a chip [4]. Here only
Computational Intelligence, Artificial Neural Networks. the modeling part has been shown using one particular and
popular motor-DC Servo Motor.
Keywords
2. COMPUTATIONAL INTELLIGENCE
Modeling, ANN, DC Servo Motor, MATLAB, Simulink. AND ARTIFICIAL NEURAL NETWORK
Computational intelligence (CI) is a set of Nature-inspired
1. INTRODUCTION computational methodologies and approaches to address
A system comprises multiple views such as planning, complex problems of the real world applications to which
requirement (analysis), design, implementation, deployment, traditional (first principles, probabilistic, black-box, etc.)
structure, behavior, input data, and output data views. A methodologies and approaches are ineffective or infeasible.
system model is required to describe and represent all these
multiple views. Modeling is the process of producing a model;
a model is a representation of the construction and working of
some system of interest. A model is similar to but simpler
than the system it represents. One purpose of a model is to
enable the analyst to predict the effect of changes to the
system. On the one hand, a model should be a close
approximation to the real system and incorporate most of its
salient features. On the other hand, it should not be so
complex that it is impossible to understand and experiment
with it. A good model is a judicious tradeoff between realism
and simplicity [1]. How is it possible to forecast electrical
load patterns for tomorrow, with access solely to today‟s load
Fig 1: An artificial neural network is an interconnected
data? How is it possible to predict the dynamic behavior of a
group of nodes
spacecraft that has yet to be built? And how is it possible to
analyze the motion and path-planning of a robotic rover that It primarily includes Fuzzy logic systems, Neural Networks
will explore on Mars surface in the next year? The answer is and Evolutionary Computation. Artiﬁcial neural nets (ANNs)
computer simulations based on mathematical models and sets can be regarded as a functional imitation of biological neural

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networks and as such they share some advantages that It‟s clear that a basic servomotor has two main components,
biological organisms have over standard computational the first is the electrical component; which consists of
systems. The main feature of an ANN is its ability to learn resistance R, inductance L, input voltage V 0(t) and the back
complex functional relations by generalizing from a limited electromotive force Vb. The second component of the
amount of training data. Neural nets can thus be used as servomotor is the mechanical part, from which we can get the
(black-box) models of nonlinear, multivariable static and useful mechanical rotational movement at the shaft. The
dynamic systems and can be trained by using input–output mechanical parts are the motor‟s shaft, inertia of the motor
data observed on the system [5]. and load inertia J and damping b. θ Refers to the angular
position of the output shaft which can be used later to find the
An Artificial Neural Network (ANN) is a mathematical or angular speed of the shaft ω.
computational model based on the structure and functional
aspects of biological neural networks. It consists of an DC Servomotors have good torque and speed characteristics;
interconnected group of artificial neurons, and it processes also they have the ability to be controlled by changing the
information using a connectionist approach to computation. voltage signal connected to the input. These characteristics
An ANN mostly is an adaptive system that changes its made them powerful actuators used everywhere. Before
structure based on external or internal information that flows modeling the motor several nonlinearities are also a matter of
through the network during the learning phase [6]. concern. Modeling these nonlinearities will make the motor
look like an original motor. One important non-linear
3. DC SERVO MOTORS behavior in servomotors is the saturation effect, in which the
The DC servo motors are presently used worldwide in output of the motor cannot reach the desired value. For
applications such as X-Y tables, factory automation, coil example, if we want to reach a 110 rpm angular speed when
winders, labeling equipment, machine tool, insertion we supply a 12 volt input voltage, but the motor can only
machines, robotics [7], pick and place, packaging, converting reach 100 rpm at this voltage. The saturation effect is very
equipment, assembly equipment and laboratory equipment. common in almost all servomotor systems. Other non-linear
Due to their importance, the design of controllers for these effect is the dead zone; in which the motor will not start to
systems has been an interesting area for researchers from all rotate until the input voltage reaches a specific minimum
over the world. For these purposes the modeling of DC value, which makes the response of the system slower and
servomotor system is an interesting area that still offers requires more controllability. A mathematical type of non-
multiple topics for research, especially after the discovery of linear effect found in the servomotors is the backlash in the
Artificial Neural Networks (ANN) and their possible usage motor gears. Some of the servomotors use internal gears
for intelligent control purposes. From this point of view and connections in order to improve their torque and speed
the importance of having efficient servomotor systems and characteristics, but this improvement comes over the effect in
experimenting with servomotors, the use of ANN plays a vital the output speed and position characteristics. The goal in this
role in modeling Servo Motors. A Servomotor system consists paper is to create a model which can mimic a practical servo
of different mechanical and electrical components, the motor and which can be used further in several applications
different components are integrated together to perform the using artificial neural networks.
function of the servomotor, Figure 2 below shows a typical
model of a servomotor system [8]. 3.1 Mathematical Description
Recalling the DC servomotor diagram from Figure 2, the
transfer function of the DC servomotor can be derived using
Kirchhoff‟s voltage law and Laplace transforms as the
following:

𝑑𝑖
𝑉𝑜 = 𝑉 𝑚 = 𝑅 𝑚 𝑖 𝑚 + 𝐿 𝑚 + 𝑉𝑏 (1)
𝑑𝑡

The Back-electromotive force (emf) Vb can be found by using
the equation shown below:

𝑑𝜃
𝑉𝑏 = 𝐾 𝑚 = 𝐾𝑚 𝜔𝑚 (2)
𝑑𝑡

Where Vb is the induced voltage, Km is the motor torque
constant, and ωm is the angular rotating speed. It can be seen
that ωm can be calculated by the Equation shown below:

𝜔𝑚 = 𝜃 (3)

And using Laplace Transform

𝜔(𝑠) = 𝑠𝜃 𝑠 (4)

The main concern in this stage is to control the angular
rotating speed ωm, by controlling the input voltage V m.
Fig 2: Servo Motor Circuit Diagram and original DC
Servo Motors (Courtesy of Baldor Servo Motors)

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Where, J = moment of inertia of the rotor; b = dampening Table 1. DC Servo Motor parameter values
ratio of the mechanical system; T = motor torque; I = current;
Vm = back emf; θ = shaft position; K = electromotive force Parameter Value
constant; ωm = measured angular speed; R = motor armature Moment of Inertia J 0.0062 N.m.s2/rad
resistance; L = inductance; V = source voltage.
Damping Coefficient b 0.001 N.m.s/rad
The transfer function of the output angular speed is derived
using Laplace transform using the second order system Torque Constant Kt 0.06 N.m/A
equation: Electromotive Force
0.06 V.s/rad
Constant Ke
ωn
G s = (5) Electrical Resistance R 2.2 Ohms
s 2 +2ξωs+ω2

Electrical Inductance L 0.5 Henry
The resulting transfer function:

ω K
= (6)
V Js+b Ls+R +K2 From the SIMULINK model it is clear that we can divide the
transfer function into two transfer functions, the first one is
From Equation 4, the relationship between the angular the electrical transfer function; which consists of the electrical
position and the speed can be found by multiplying the resistance and the inductance. The second transfer function is
angular position by 1/s. Figure 3 shows the block diagram the mechanical transfer function; which consists of the
which represents the servomotor system using MATLAB and moment of inertia and the damping coefficient. By dividing
SIMULINK. the transfer function into the two parts mentioned above, we
can add the non-linear parameters to the system to see their
Voltage V(s) Load effect. The dead zone value was 1.5 volts, which is very
common in this size of servomotors (12 Volts).
Torque Velocity
𝐾 1 1
𝐿𝑠 + 𝑅 𝐽𝑠 + 𝑏 𝑠
4. SIMULINK MODEL
Simulink is a software package for modeling, simulating, and
analyzing dynamical systems. It supports linear and nonlinear
Armature Angle systems, modeled in continuous time, sampled time, or a
hybrid of the two. Systems can also be multi-rate, i.e., have
Back E mf Vb(s) different parts that are sampled or updated at different rates.
K Models here are hierarchical. This approach provides insight
into how a model is organized and how its parts interact. After
someone defines a model, he/she can simulate it, using a
Fig 3: Mathematical block diagram of Servo Motor choice of integration methods, either from the Simulink
The parameter values used in the SIMULINK model were menus or by entering commands in MATLAB's command
taken from a practical servomotor (Baldor Servo Motors). The window.
parameters are given in Table 1:

Fig 4: DC Servo Motor Model (Simulink Environment)

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In this paper Simulink 7.0 (MATLAB R2007b) was used for Here, fig 5 shows the input and fig 6 shows the dead zone of
modeling purpose. At first the DC Servo Motor model was the motor after simulation. The main idea was to take these
created according to the mathematical description of section input and output points, feed the inputs into neural networks.
3. The model (Fig 4) was derived from the Servomotor speed The neural networks are very good at showing the outputs if
transfer function (Equation 6). Simulink‟s “To Workspace” sufficient input points are provided. This way the neural
block was used to take input and output value of the motor network itself will become like the DC Servo motor.
model. The simulation took 10 sec.

Fig 5: Input Signal (Sine wave of 6 rad/s) of the Motor (Using Scope)

Fig 6 : Dead Zone Effect in Motor which is limiting output to 10.5 V (Using Scope)

5. NN IN MODELING
Using MATLAB command window several neural networks neurons with „tansig‟ function and layer had „purelin‟
were created and examined. Before creating networks data function. The maximum number of epochs used was 1000,
were normalized between values -1 to 1 to avoid convergence which is the maximum number of trials the training method
problem writing the following lines in a .m file: can apply before stopping.

dataout = datain - min(datain(:)); The training goal was to reach a minimum error value of
dataout = (dataout/range(dataout(:)))*(maxval-minval); 0.00005; this error value was between the input signal and the
dataout = dataout + minval; generated output. The learning rate was chosen to be 0.05.
These parameters were chosen to best fit the performances of
The inputs were taken into P and the outputs were taken into the network, more restrict parameters may take the network to
T matrix. T was the target matrix. Hidden layer had 10 have unstable response and it may cause the training method
to diverge. Thus different network architecture‟s were created
and examined. The following results were found:

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Fig 7 : Output of Motor (Using Scope)

Fig 8: Output of Motor using NN (Before Training)

Fig 9: Performance goal met
Comparing figure 7 and 8, it is clear that the neural network So after the successful training the performance goal met fast
couldn‟t reflect the exact output. So to mimic the behavior (6 epochs). From the following figures it can be shown that
correctly training parameters were given in the command the network has realized the problem well enough.
window.

47


Comparing figure 7 and 10, it is clear that the network was The following table shows the complete result from all
able to mimic the original behavior almost successfully. The networks:
human eye would not be able to find the difference between
two outputs but if we plot both original motor and NN motor Table 2. Complete Result from different networks
model output (overlapped) then some clear difference will
come out (Fig 11) which can be further minimized using Neural Training
MSE
algorithms like Genetic Algorithm, Particle Swarm Network Function
Optimization, and Ant Colony Optimization [9]. Feed-Forward 1.20611e-6 (goal met in 6
Trainlm
Backprop epochs)
Several architectures were examined and feed-forward Elman 0.0474668 (goal didn‟t met
backpropagation with „trainlm‟ gave the lowest error (MSE). Backprop
Traingdx
in 1000 epochs)
These previous figures were all taken from feed-forward
backpropagation network which was best network for this Elman 0.137859 (goal didn‟t met in
Traingd
problem. Fig 12 shows problems with other Neural Networks. Backprop 1000 epochs)
Cascade
0.0116465 (goal didn‟t met
Forward Traingda
in 1000 epochs)
Backprop

Fig 10: Output of Motor (After Training) (Feed-Forward Backprop with
Trainlm)

Fig 11: Overlapped Outputs showing minor errors (Original and NN
model)

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Fig12: Unlike Feed-Forward Backprop some network showed poor result
(Original and NN Elman backprop model with Traingdx; Elman NN in Green)

6. CONCLUSION DSP based implementation is sequential and hence does not
This paper presents modeling of a motor (DC Servo Motor) preserve the parallel architecture of the neurons in a layer.
and Artificial Neural Networks in mimicking its exact ASIC implementations do not offer re-configurability by the
behavior. The result showed that feed-forward user. In future this model can be further implemented in VLSI
backpropagation neural network worked very well compared architectures like FPGA using Hardware Description
to other networks in copying the behavior of the original Languages and that particular IC or chip could represent the
motor. Meta-heuristic algorithms like PSO, ACO, GA original motor in various innovative applications. FPGA is a
[10][11][12] could further minimize the error. suitable hardware for neural network implementation as it
preserves the parallel architecture of the neurons in a layer
Real time applications are possible only if low cost high- and offers flexibility in reconfiguration.
speed neural computation is made realizable. Towards this
goal numerous works on implementation of Neural Networks Because of superior agility and flexibility, robotic rovers are
(NN) have been proposed [13]. Neural networks can be very popular and widely used by NASA in their various
implemented using analog or digital systems. planetary missions (Lunar missions, Mars missions) for
surface navigation. DC Servo Motors play a vital role here.
The digital implementation is more popular as it has the Working with original DC Motors time and time again in
advantage of higher accuracy, better repeatability, lower noise planetary experiments before final missions might become
sensitivity, better testability, higher flexibility, and costly. In these case the above presented technique could
compatibility with other types of preprocessors. The digital become handy. Present day systems are large and complex.
NN hardware implementations are further classified as FPGA- Putting their behavior inside Integrated Circuits using this
based implementations, DSP-based implementation, ASIC- kind of technique could become a useful tool for professional
based implementations[14-15]. engineers.

49


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Application of CI in Motor Modeling

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