DC Position Control System – Determination of Parameters and Significance on System Dynamics

ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 01, Feb 2012

DC Position Control System – Determination of
Parameters and Significance on System Dynamics
C.Ganesh 1, B.Abhi 2, V.P.Anand3, S.Aravind4, R.Nandhini5 and S.K.Patnaik6
1,2,3,4,5
Sri Ramakrishna Institute of Technology, Coimbatore, India
Email: c.ganesh.mtech72@gmail.com
6
College of Engineering, Guindy, Chennai, India

Abstract—Physical systems used for control applications without considering the load parameters [9]-[13], then such a
require proper control methodologies to obtain the desired system will not yield desired response in real time. Precision
response. Controller parameters used in such applications and accuracy are of utmost importance in tuning controller
have to be tuned properly for obtaining the desired response parameters to achieve the desired transient and steady state
from the systems. Tuning controller parameters depends on
responses without sacrificing stability. Hence determination
the physical parameters of the systems. Therefore, the physical
parameters of the systems have to be known. Number of of mechanical parameters of motor and load by employing
techniques has been developed for finding the mechanical appropriate techniques is of utmost importance. The
parameters of motors. But, no straightforward method has controller tuning was done taking into account mechanical
been established for estimating the parameters of the load so parameters of motor as well as load in which inertia and friction
far. This paper presents a method of determining mechanical are either already known or specified [14]-[19]. However,
parameters viz. moment of inertia and friction coefficient of variation of load parameters under dynamic load variation
motor & load. This paper also stresses that load parameters was not accounted [14]-[19].
have appreciable effect on the dynamic response of systems Most of the control applications employ motor and
and have to be determined. A DC servo position control system
mechanical load arrangement. Hence, simple and standard
is considered for applying the method. Moment of inertia and
friction coefficient of the DC servo motor as well as load are strategies are the order of the day to compute the moment of
determined using the method. It is evident that moment of inertia and friction coefficient of motor and load. So far, no
inertia and friction coefficient can be determined for any load simple strategies have been developed to estimate inertia
arrangement using the proposed method. Effect of load on the and friction. Further, the effect of variation of these
system dynamics is emphasized by considering the PID parameters with respect to dynamic load variation on the
controller tuning. It is found that PID controller when tuned system behavior has not been highlighted so far. This paper
based on estimated load parameters could yield optimum presents a very simple and standard procedure to determine
response. This justifies that load parameters have to be the moment of inertia and friction coefficient of DC motor
determined for dynamic load variations.
and load under dynamic load variations. Moreover, the effect
Index Terms— Inertia, Friction, Back emf, PID controller of load on the system behavior is also highlighted with suitable
case studies under dynamic load variations.
I. INTRODUCTION
II. DETERMINATION OF PARAMETERS
Identification of parameters of any physical system plays
a vital role to choose the parameters of controllers A. Importance of Estimation of Dynamic Parameters
appropriately. This is essential to make sure that the system Parameters of the DC servomotor such as torque constant
controlled satisfies the desired performance specifications. KT, back emf constant Kb, armature resistance Ra, armature
Over the years, a great deal of research has been carried out inductance La, moment of inertia of motor and load J, friction
in the estimation of parameters of systems using genetic coefficient of the motor and load B have to be estimated
algorithms, fuzzy logic and neural networks. Inertia and properly so that controller parameters can be properly tuned
Friction coefficient of motor alone were determined but that and the desired response can be achieved from the DC
of load were not considered even though optimization, position control system. KT, Kb, Ra and La do not vary with
adaptive control and artificial intelligent techniques were load and hence these values are determined using
used [1]-[5]. The importance of estimation of load parameters conventional method. However, J and B vary with respect to
was emphasized in [6] but strategies for estimating inertia load as per the details given in the subsections C and D.
and friction of load were not highlighted. Even in precise Hence, their variations will have an effect on the dynamics of
applications such as position control, viscous friction of the system.
motor was estimated [7] but that of load was not at all taken DC servomotor used for illustration of the determination
into consideration. In [8], load model parameters were of parameters has the ratings: 24V, 4A, 4000rpm, 12.6&! armature
obtained using genetic algorithm but friction coefficient of resistance (Ra) and 283mH armature inductance (La).
motor was not at all considered. Tuning controller parameters
B. Determination of Torque Constant
demands proper estimation of physical parameters of systems.
If controller tuning is done based on only motor parameters In armature control method, the armature voltage and
© 2012 ACEEE 1
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hence the armature current are varied. Back emf is calculated load current using “(8)”.
using the expression DC servomotor is switched on at no load. The motor is
E b  Va  i a R a . (1) loaded in steps. At each load current, steady state values of
armature current and speed are noted. B is determined at
The value of angular speed  is determined from the value of
each load using “(8)”. These values are tabulated in Table II.
measured speed N in rpm. Back emf is proportional to speed.
TABLE II. E STIMATION OF B
Eb  K b . (2)
The slope of the graph obtained by plotting the variation of
back emf Eb against speed  gives the value of Kb. The
mechanical equivalent of electrical power and mechanical
power are equal at steady state.
Te  E b i a . (3)
Electromagnetic torque Te is proportional to armature current D. Determination of Moment of Inertia
ia. Therefore, When the supply to the armature is switched off, motor
Te  K T i a . (4) speed reduces to zero from its steady speed. Hence, the torque
where KT is the torque constant. From “(2)”, “(3)” and “(4)”, equation becomes
it can be obtained that d
J  B  0 . (9)
Kb  KT . (5) dt
Hence, Torque constant KT is obtained from the slope of the The solution for “(9)” obtained using the steady state speed
graph obtained by plotting the variation of Eb against ω. DC as the initial value of speed is expressed by
servomotor with the ratings as already mentioned above is Te ( B / J) t
switched on at no load. The armature voltage and hence the  e . (10)
B
armature current are varied by armature control method and
the corresponding values of speed are noted. Values of ω When t= =J/B, mechanical time constant of the motor, the
and Eb are calculated at each armature voltage and current. motor speed reduces from steady state speed to 36.8% of
They are tabulated in Table I. From the Table I, it can be steady state speed. The time taken for speed of the motor to
found that KT for the servomotor is 0.04 Nm/A. reduce from steady state speed to 36.8% of steady state speed
gives the mechanical time constant of the motor and load.
TABLE I. ESTIMATION OF KT From the time constant, the moment of inertia of the motor
and load is given by,
J  B . (11)
Thus the moment of inertia of motor and load J can be
determined by substituting the values of B and mechanical
time constant  in “(11)”.
DC servomotor is run at no load and two different load
currents. Armature current and speed are measured at each
load current. Whenever the motor is switched off, speed
response is captured on the Digital Storage Oscilloscope.
Speed responses are captured at no load and other two load
currents. They are shown in Fig. 1 and Fig. 2 respectively.
C. Estimation of Friction Coefficient
From these responses, time taken (mechanical time constant)
The torque equation of the motor and load arrangement for the speed to drop from its steady state initial speed to
is given by 36.8% of its steady state initial speed is noted for no load and
d two different loads. J is determined for each case using “(11)”.
Te  J  B . (6) These values are tabulated in Table III.
dt
where J and B are inertia and friction coefficient of the TABLE III. ESTIMATION OF J
arrangement respectively. When the speed is constant, the
torque equation becomes
Te  B . (7)
From “(4)” and “(7)”,
K Ti a
B . (8)

where ia is the armature current measured at steady state for
the given load current. Thus B is determined for the given
© 2012 ACEEE 2
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Transfer function of DC position control system at no load is
obtained by substituting the estimated parameters of DC
servomotor and load arrangement in “(12)”. It is given by

 (s) 0.04

Va (s) s[(12.6  0.283s)(2.26e  5s  2.261e  5)  0.0016] .
Using the above expression, step response of the DC position
control system is determined by MATLAB simulation and
shown in Fig. 4. Transfer function of DC position control
system at load 1 is obtained as
 ( s) 0 .04
 .
V a ( s ) s[(12 . 6  0 .283 s )(1 .94 e  5 s  4 . 52 e  5 )  0 . 0016 ]
Using the above expression, step response of the DC position
control system is determined by MATLAB simulation and
shown in Fig. 5. From Fig. 4 and Fig. 5, it is very clear that the
response of DC position control system depends on the load
Figure 1. Speed response at no load current. These simulation results are shown in Table IV. From
the Table IV, it is clear that the performance specifications
depend on the load current. Hence, apart from mechanical
parameters viz. inertia and friction of motor, mechanical
parameters of the load also have to be determined for
evaluating the response.(i.e. Inertia and friction of the load
get added to that of motor to obtain the net inertia of the
motor and load arrangement).

Figure 2. Speed response at load 1

III. E FFECT OF LOAD ON CONTROLLER TUNING AND SYSTEM
DYNAMICS
DC position control system is considered for this analysis.
Block diagram of DC motor used in position control is shown
in Fig. 3. Transfer function of the DC position control system
[20] is given by
(s) KT

Va (s) s[(Ra  sLa )(Js  B)  KbKT ] . (12)
Figure 4. Step response of position control system at no load

Figure 3. Block diagram of DC Motor
© 2012 ACEEE 3
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Figure 5. Step response of position control system at load 1
TABLE I. SIMULATION RESULTS OF DC POSITION CONTROL SYSTEM Figure 7. Step response of PID controlled system at load1

Response of the DC position control system with the use of
PID controller is optimised at no load by PARR tuning [21]
and shown in Fig. 6. Response of the DC position control
system with the use of PID controller is optimised at load 1
and shown in Fig. 7. Response of the DC position control
system with the use of PID controller is optimised at load 2
and shown in Fig. 8. These results are tabulated in Table V.
From the Table V, it is clear that PID controller parameters are
different at different load currents and have to be tuned based
on the mechanical parameters of the motor and load at a
particular load setting.

Figure 8. Step response of PID controlled system at load 2
TABLE V. SIMULATION RESULTS OF PID CONTROLLED
DC POSITION CONTROL SYSTEM

Analysis of the simulation results from Table IV and Table V
clearly reveal that load has effect on system dynamics because
mechanical parameters J and B depend on the load setting
and have to be accurately determined for evaluating the
system response and tuning the controller parameters.
Figure 6. Step response of PID controlled system at no load
© 2012 ACEEE 4
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CONCLUSIONS [7] Ricardo Campa, Elio Torres, Francisco Salas, and V´ýctor
Santib´a˜nez, “On Modeling and Parameter Estimation of Brushless
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This method can be extended to on-line parameter a Linear Brushless DC Motor,” World Academy of Science,
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DC Position Control System – Determination of Parameters and Significance on System Dynamics

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DC Position Control System – Determination of Parameters and Significance on System Dynamics