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


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


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




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


                          CONCLUSIONS                                   [7] Ricardo Campa, Elio Torres, Francisco Salas, and V´ýctor
                                                                        Santib´a˜nez, “On Modeling and Parameter Estimation of Brushless
    Proposed method can be used for estimation of moment                DC Servoactuators for Position Control Tasks,” 17th World
of inertia and friction of DC motor and load under dynamic              Congress, The International Federation of Automatic Control, Seoul,
load variations. From the illustrative studies made on DC               Korea, pp.2312– 2317, July 2008.
servo motor, it is found that inertia and friction of motor and         [8] Pei Zhang and Hua Bai, “Derivation of Load Model Parameters
load can be accurately determined using the proposed                    using Improved Genetic Algorithm,” Third International Conference
method. From the study of effect of load on the performance             on Electric utility deregulation and restructuring and Power
                                                                        technologies (DRPT2008), Nanjuing, China, pp. 970– 977, April
of DC position control system, it is found that these
                                                                        2008.
parameters have to be determined for any change in load and             [9] Mehdi Nasri, Hossein Nezamabadi-pour, and Malihe
controller parameters have to be tuned accordingly.                     Maghfoori, “A PSO-Based Optimum Design of PID Controller for
    This method can be extended to on-line parameter                    a Linear Brushless DC Motor,” World Academy of Science,
estimation of inertia and friction of DC motors with any type           Engineering and Technology, vol. 26, pp. 211– 215, 2007.
of load arrangement. There is no need to have information               [10] Gaddam Mallesham, K.B. Venkata Ramana, “Improvement in
about inertia and friction well in advance. Further, controller         Dynamic Response of Electrical Machines with PID and Fuzzy
parameters can be tuned from estimated parameters of inertia            Logic Based Controllers,” World Congress on Engineering and
and friction of motor and load by employing artificial                  Computer Science (WCECS 2007), San Francisco, USA, October
                                                                        2007.
intelligent techniques. This will improve the response of the
                                                                        [11] B.Nagaraj and N.Murugananth, “Soft-Computing Based
system in real time whenever there is a change in load.                 Optimum design of PID controller for position control of DC
    This method can be also extended to on-line parameter               motor,” ACTA Electrotechnica, vol.51, pp. 21– 24, 2010.
estimation of inertia and friction of induction and synchronous         [12] Chih-Cheng Kao, Chin-Wen Chuang, Rong-Fong Fung, “The
motors with any type of load arrangement, if torque equation            self-tuning PID control in a slider–crank mechanism system by
of DC motor is replaced by that of induction or synchronous             applying particle swarm optimization approach,” Mechatronics,
motor.                                                                  vol. 16, pp. 513–522, October 2006.
                                                                        [13] M.B.B. Sharifian, R.Rahnavard and H.Delavari, “Velocity
                          REFERENCES                                    Control of DC Motor Based Intelligent methods and Optimal Integral
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[1] Radu Babau, Ion Boldea, T. J. E. Miller and Nicolae Muntean,        Theory and Engineering, vol. 1, pp. 81– 84, April 2009.
“Complete Parameter Identification of Large Induction Machines          [14] Mohamed A. Awadallah, Ehab H. E. Bayoumi and Hisham M.
from No-Load Acceleration – Deceleration Tests,” IEEE                   Soliman, “Adaptive Deadbeat Controllers for Brushless DC Drives
Transactions on Industrial Electronics, vol. 54, pp. 1962-1972,         Using PSO and ANFIS Techniques,” Journal of Electrical
August 2007.                                                            Engineering, vol. 60, pp. 3–11, 2009.
[2] Arif A. Al-Qassar, Mazin Z. Othman, “Experimental                   [15] Sakda Prommeuan, Sitchai Boonpiyathud and Tianchai Suksri,
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Motor Using Genetic Elman Neural Network,” Journal of                   System,” ICCAS-SICE International Joint Conference 2009,
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2008.                                                                   [16] Muammer Gokbulut, Besir Dandil, Cafer Bal, “Development
[3] Marin Despalatoviæ, Martin Jadriæ, Božo Terziæ,                     and Implementation of a fuzzy-neural network controller for
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Acceleration and Deceleration Tests,” Automatika, vol. 46, pp.          vol. 13, pp. 423– 435, 2007.
123–128, January 2006.                                                  [17] L. Canan Dulger and Ali Kirecci, “Motion Control and
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dynamic model parameters of a BLDC motor,” Simulation                   Simulation In Engineering, vol. 2, pp. 1– 6, January 2007.
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[5] M. Hadef, A.Bourouina, M.R.Mekideche, “Parameter                    for aerofin control with a pwm controlled DC motor,” Automatic
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[6] Whei-Min Lin, Tzu-Jung Su, Rong-Ching Wu and Jong-Ian               Synchronous Motor Servo System,” International Conference on
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Applications(ICEA), Taichung, Taiwan, pp.1762– 1767, June 2010.         [20] Norman S. Nise, Control Systems Engineering, The Benjamin/
                                                                        Cimmins Publisihng Company, Inc, 5th edition, 2008.
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                                                                        Edinburg: BSP Professional Books, 1989.




© 2012 ACEEE                                                        5
DOI: 01.IJEPE.03.01. 82

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

  • 1. 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 DOI: 01.IJEPE.03.01. 82
  • 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 01, Feb 2012 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 DOI: 01.IJEPE.03.01. 82
  • 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 01, Feb 2012 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 DOI: 01.IJEPE.03.01. 82
  • 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 01, Feb 2012 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 DOI: 01.IJEPE.03.01. 82
  • 5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 01, Feb 2012 CONCLUSIONS [7] Ricardo Campa, Elio Torres, Francisco Salas, and V´ýctor Santib´a˜nez, “On Modeling and Parameter Estimation of Brushless Proposed method can be used for estimation of moment DC Servoactuators for Position Control Tasks,” 17th World of inertia and friction of DC motor and load under dynamic Congress, The International Federation of Automatic Control, Seoul, load variations. From the illustrative studies made on DC Korea, pp.2312– 2317, July 2008. servo motor, it is found that inertia and friction of motor and [8] Pei Zhang and Hua Bai, “Derivation of Load Model Parameters load can be accurately determined using the proposed using Improved Genetic Algorithm,” Third International Conference method. From the study of effect of load on the performance on Electric utility deregulation and restructuring and Power technologies (DRPT2008), Nanjuing, China, pp. 970– 977, April of DC position control system, it is found that these 2008. parameters have to be determined for any change in load and [9] Mehdi Nasri, Hossein Nezamabadi-pour, and Malihe controller parameters have to be tuned accordingly. Maghfoori, “A PSO-Based Optimum Design of PID Controller for This method can be extended to on-line parameter a Linear Brushless DC Motor,” World Academy of Science, estimation of inertia and friction of DC motors with any type Engineering and Technology, vol. 26, pp. 211– 215, 2007. of load arrangement. There is no need to have information [10] Gaddam Mallesham, K.B. Venkata Ramana, “Improvement in about inertia and friction well in advance. Further, controller Dynamic Response of Electrical Machines with PID and Fuzzy parameters can be tuned from estimated parameters of inertia Logic Based Controllers,” World Congress on Engineering and and friction of motor and load by employing artificial Computer Science (WCECS 2007), San Francisco, USA, October 2007. intelligent techniques. This will improve the response of the [11] B.Nagaraj and N.Murugananth, “Soft-Computing Based system in real time whenever there is a change in load. Optimum design of PID controller for position control of DC This method can be also extended to on-line parameter motor,” ACTA Electrotechnica, vol.51, pp. 21– 24, 2010. estimation of inertia and friction of induction and synchronous [12] Chih-Cheng Kao, Chin-Wen Chuang, Rong-Fong Fung, “The motors with any type of load arrangement, if torque equation self-tuning PID control in a slider–crank mechanism system by of DC motor is replaced by that of induction or synchronous applying particle swarm optimization approach,” Mechatronics, motor. vol. 16, pp. 513–522, October 2006. [13] M.B.B. Sharifian, R.Rahnavard and H.Delavari, “Velocity REFERENCES Control of DC Motor Based Intelligent methods and Optimal Integral State Feedback Controller,” International Journal of Computer [1] Radu Babau, Ion Boldea, T. J. E. Miller and Nicolae Muntean, Theory and Engineering, vol. 1, pp. 81– 84, April 2009. “Complete Parameter Identification of Large Induction Machines [14] Mohamed A. 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[16] Muammer Gokbulut, Besir Dandil, Cafer Bal, “Development [3] Marin Despalatoviæ, Martin Jadriæ, Božo Terziæ, and Implementation of a fuzzy-neural network controller for “Identification of Induction Motor Parameters from Free brushless DC drives,” Intelligent Automation and Soft Computing, Acceleration and Deceleration Tests,” Automatika, vol. 46, pp. vol. 13, pp. 423– 435, 2007. 123–128, January 2006. [17] L. Canan Dulger and Ali Kirecci, “Motion Control and [4] A. Kapun, M. Èurkoviè, A. Hace and K. Jezernik, “Identifying Implementation for an AC Servomotor System,” Modelling and dynamic model parameters of a BLDC motor,” Simulation Simulation In Engineering, vol. 2, pp. 1– 6, January 2007. Modelling Practice and Theory, vol.16, pp. 1254–1265, October [18] Milan R. Ristanoviæ, Dragan V. Laziæ, Ivica Inðin, “Nonlinear 2008. PID controller modification of the electromechanical actuator system [5] M. Hadef, A.Bourouina, M.R.Mekideche, “Parameter for aerofin control with a pwm controlled DC motor,” Automatic identification of a DC motor using Moments method,” International Control and Robotics, vol. 7, pp. 131 – 139, 2008. Journal of Electrical and Power Engineering, vol.1, pp. 210– 214, [19] Aimeng Wang, Wenqiang Xu , Cheng-Tsung Liu, “On-Line PI 2007. Self-Tuning Based on Inertia Identification For Permanent Magnet [6] Whei-Min Lin, Tzu-Jung Su, Rong-Ching Wu and Jong-Ian Synchronous Motor Servo System,” International Conference on Tsai, “Parameter Estimation of Induction Machines Under No- Power Electronics and Drives Systems, PEDS 2009, Taipei, Taiwan, Load Test,” 5th IEEE Conference on Industrial Electronics and pp. 1406– 1410, November 2009. Applications(ICEA), Taichung, Taiwan, pp.1762– 1767, June 2010. [20] Norman S. Nise, Control Systems Engineering, The Benjamin/ Cimmins Publisihng Company, Inc, 5th edition, 2008. [21] E.A. Parr, Industrial Control Handbook, vol. 3, Oxford, Edinburg: BSP Professional Books, 1989. © 2012 ACEEE 5 DOI: 01.IJEPE.03.01. 82