International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved
54
Speed Control of DC Motor using PID Controller with Buck Converter as Final control Element
Gagan Madan1, Gunjan V Sahai2
Department of Electrical Engineering DIT University Dehradun, India
[email protected] [email protected]
Abstract — For a huge assortment of Industrial applications dc motors are being utilized. The normal necessity of the drives in commercial ventures is speed control under shifting working conditions. In a few exploration thinks about, the controllers have been considered without demonstrating of final control element (FCE). In practical applications, the impact of dynamics and nonlinearity of FCE influences the execution of the framework, so it is important to consider these for a reliable recreation investigation of the drive execution. The general framework gets to be non-straight because of the dynamics of converter utilized as FCE. In this study another methodology is being utilized, first the transfer function of the buck converter is acquired by Considering a small region close to the working point, then utilizing general exchange capacity of buck converter and dc motor PID controller will be balanced.
Presently NN is utilized to upgrade these settings on-line relating to the progressions that may happen in framework working conditions. This setup of controller is additionally seen to have powerful execution against parameter varieties and instabilities.
For all the more near real execution assessment PWM controlled buck converter, utilized as FCE has been recreated utilizing sim- power framework library of MATLAB.
1. Introduction
For an extensive assortment of modern applications DC motor have been utilized generally. The normal necessity of the drives utilized as a part of commercial ventures is speed control under changing working conditions. In a few examination contemplates, the controller have been utilized without displaying of Final Control component (FCE). In practical applications the effect of dynamics and nonlinearity of FCE changes the execution of the framework. So it is important to consider it for tried and true investigation of the motor.
In 90's Fuzzy Logic was in its full grown state and analysts overall depended on learning based versatile control utilizing FUZZY standards, with the coming of Neural Network for model free and powerful control, scientists distrustfully utilized it as a part of procedure control and results turned out promising. J.F. Cavalcanti [2] recommended Adaptive control of a dynamic framework spoke to by a D.C. Motor. The framework depended on PID and Neural Network and uses
FUZZY tenets to switch between the two controllers. Direct nonlinear Adaptive state controller taking into account dynamic Neural Network was determined by G.A.Rovithakis, M.A. Christodoulou [3], and it was effectively connected to control the sped of a non linearized DC Motor, one fascinating component of the proposed control calculation was that it covers the circumstance where the attractive flux consistently changes, as iut was the situation in the misfortune minimization issue. Comparative work had been accounted for by M.D. Minkova, Et Al [4]. El-Sharkawi and El-Samahy [1]
has proposed a multi-layer Neural Network(NN) construction modeling for the distinguishing proof and control of DC Brushless motors working in an elite drives environment. N.A.
Ahmed [5] recommended a dynamic model and relentless state equal circuit of a solitary phae AC-DC buck-boost converter fed DC Motor with uniform PWM control was displayed. The waveforms of voltage and current, the information and yield attributes of the converter were completely talked about and checked. Some different specialists likewise reported comparative results [6-8].
Present study depends on the work done by S. Sheel and Omhari [9]. They had taken a DC Motor drive with Buck converter as a Final Control Element. A PID controller is tuned by ZN tuning system. The present study broadens the work done in [9] by utilizing EMRAN-RBF basic versatile Neural Network controller. The fundamental point of interest of this study over past studies reported so far is that, in the above works intermittent NN in light of Back Propagation is utilized which regularly get stuck in local minima also the time taken is large. Work done in [9] suggested a fixed gain controller the results of the proposed controller are compared with that in [9].
2. Buck converter design
A chopper is a static power electronic device which converts fixed dc input voltage to a variable dc output voltage. It can be step up or step down. It is also considered as a dc equivalent of an ac transformer since they behave in an identical manner.
Due to its one stage conversion, choppers are more efficient and are now being used all over the world for rapid transit systems, in marine hoist, in trolley cars, in mine haulers and in
International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved
55
forklift trucks etc. The future electric automobiles are likely to use choppers for their speed control and braking. Chopper systems offer smooth control, high efficiency, faster response and regeneration facility.
Fig.1 Buck chopper
The Output equation of the buck converter in terms of the input voltage and duty ratio of the switch is given as:
V=DVd
The design of buck converter is based on the output voltage (V), maximum allowed ripple in the output voltage or capacitor voltage (△Vc), load current (I0) and maximum allowed ripple in the inductor current (△IL). Based on these the values of the buck converter parameters (i.e. inductor and capacitor used in the buck converter) can be obtain as
following. The value of inductance will be:
(1 )
d l
DV D L f I
The capacitance can be calculated as:
2
(1 ) 8
d c
DV D C Lf V
For continuous conduction of the converter there must be a check, which can be performed by verifying the values of inductance and capacitance.
i.e.
2
(1 )
2 ;
(1 )
16 L D R
f C D
Lf
The power semiconductor devices used for a chopper circuit can be force commutated thyristor, BJT, MOSFET, IGBT and GTO. These devices are generally represented by a switch. When the switch is OFF, no current will flow. Current flows through the load when switch is ON. The power semiconductor devices have on-state voltage drop of 0.5V to 2.5V across them. For the sake of simplicity, this voltage drop across these devices is generally neglected.
Fig. 2. Operation of Chopper and its Waveforms
During Period Ton, Chopper is ON and load voltage is equal to source voltage Vs. During the interval Toff ,chopper is OFF, load current flows through the freewheeling diode FD. As a result, load terminals are short circuited by FD and load voltage is therefore, zero during Toff. During Ton, load current rises whereas during Toff load current decays.
3. Mathematical Model of the DC motor
For the separately excited DC motor model [35] considered for study as in fig. 4. The voltage equation of the armature circuit under transient is given by:
a a a
di
a mV R i L K
dt
Here
K K
e
From the dynamics of motor load system
m
L m
J d T T B
dt
Here
T Ki
aSo
d
m a L mJ Ki T B
dt
Differentiating equation 6.2 gives
2 2
a m m L
di d d dT
K J B
dt dt dt dt
Taking Laplace of this equation and solving for ωm
2 2
1 2 1 2
( / ) (1 )
1 1 ;
[ (1 )] [ (1 )]
a ma
m L
a a
a a
m m m m
K R s
T
J s s J s s
Where ;
1 2 2
; ;
2
;
a
e e a
a
a
m m
a
PZ L
K K K
A R
JR J
B BR K
International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved
56
For the purpose of study a separately excited dc motor with nameplate ratings of 1 hp, 220 V, 550 rpm has been used in simulation. Following parameter values are associated with it. Moment of Inertia, J = 0.068 kg-m2 or Nm/ (rad/sec2);
Coefficient of viscous friction, B=0.03475 Nm-sec or Nm/(rad/sec); Armature resistance, Ra=7.56 ohms;
Armature circuit inductance, La = 0.055 Henry; K = 3.475 V/rad/sec; τa=0.00727 Sec; τm1=1.9568 Sec; τm2=2 Sec.
With full load torque of 12.95 Nm Substituting the values in the equation (7), the speed of the motor can be expressed as a function of supply voltage and load torque as:
2 2
929.8 14.7 2022.81
( ) ( )
138 3354.91 138 3354.91
m L
V s s T s
s s s s
Fig. 3. Separately excited DC motor
PID gains setting using ZN Reaction curve Method [9] are been included in TABLE I.
4. PID Controller
There are different types of controller available and its selection is also an important work. Some of the controllers which are most widely used are – proportional controller ,on–
off controller, integral controller, derivative controller and PID controller. In proportional controller error speed is proportional to the measured output. This controller has the limited use and can never force the motor to run exactly at the set point speed. Therefore an improvement is required for correction in the output. In PI controller, the proportional term does the job of fast correction and the integral term takes finite time to act and makes the steady state error zero. In
derivative approach further refinement is done. This controller will allow the rate of change of error speed to apply an additional correction to the output drive. It can be used to give a very fast response to sudden changes in motor speed. In simple PID controllers it becomes very difficult to generate a derivative term in the output that has any significant effect on speed of motor. It can be deployed to reduce the rapid speed oscillation caused by high proportional gain. Therefore, in many controllers, it is not used. The derivative action causes the noise (random error) in the main signal to be amplified and reflected in the controller output. Hence the most suitable controller for speed control is PI type controller.
Proportional-Integral-Derivative (PID) controllers [1][3]
are widely used in industrial control systems because of the reduced number of parameters to be tuned. They provide control signals that are proportional to the error between the reference signal and the actual output (proportional action), to the integral of the error (integral action), and to the derivative of the error (derivative action), namely
Where u(t) and e(t) denote the control and the error signals respectively, and Kp, 'Ii and Td are the parameters to be tuned.
The corresponding transfer function is given as
These functions have been enough to the most control processes. Because the structure of PID controller is simple, it is the most extensive control method to be used in industry so far. The PID controller is mainly to adjust an appropriate proportional gain ( K p ), integral gain (K [ ), and differential gain (KD) to achieve the optimal control performance. The PID controller system block diagram of this paper is shown in Figure 2.
Fig. 4. PID controller block diagram Transfer function can also be expressed as
The main features of PID controllers are the capacity to eliminate steady-state error of the response to a step reference signal (because of integral action) and the ability to anticipate output changes (when derivative action is employed).
International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved
57
5. Simulation and Results
Fig. 5. Reference Speed and Motor Speed
Fig. 6. Simulink Model of Chopper fed DC Motor with PID Controller Rating of the elements used in above simulation:
DC input voltage – 240 V
DC machine rating – 5HP, 240 V, 1750rpm Applied field voltage – 300 V
Torque of 10 N-m is applied @ 1 sec , L – 10mH
After simulation of the above model we are getting a graph of armature speed, armature current, electrical torque and armature voltage with respect to time.
International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved
58
Fig. 7. Motor speed, Armature Current and Electrical Torque Table 2
DC Motor Specifications
Parameter Value
Nominal Armature Voltage 240V
Nominal Field Voltage 300V
Armature Resistance 2.581 ohm
Armature Inductance 0.028 H
Field Resistance 281.3 ohm
Field Inductance 156 H
Mutual Inductance 0.9483 H
Nominal Speed 1750 RPM
Nominal Torque 2.26 N-m
When the load is constant the speed response is smooth after attaining steady state. When load is constant and reference speed is varying then speed response is shifting accordingly with a time delay. But when the load is varying, speed response have ripples due to time delay in achieving desired speed. When Reference speed and load is varying then in speed response, there is some ripple due to delay in achieving current reference speed. After connecting optimizing filter the over shoot is reduced and speed response is enhanced.
Chopper systems offer smooth control, high efficiency, faster response and regeneration facility.
6. Performance Measures Mean absolute error (MAE)
The MAE measures the average magnitude of the errors in a set of forecasts, without considering their direction. It measures accuracy for continuous variables. The MAE is the average over the verification sample of the absolute values of the differences between forecast and the corresponding observation. The MAE is a linear score which means that all the individual differences are weighted equally in the average.
Conclusion
The speed of a dc motor has been successfully controlled by using Chopper as a converter and Proportional-Integral type Speed and Current controller based on the closed loop model of DC motor. Initially a simplified closed loop model for speed control of DC motor is considered and requirement of current controller is studied. Then a generalized modelling of dc motor is done. After that a complete layout of DC drive system is obtained. Then designing of current and speed controller is done. Now the simulation is done in MATLAB under varying load condition, varying reference speed condition and varying input voltage. The results are also studied and analyzed under above mentioned conditions. The model shows good results under all conditions employed during simulation.
Since, the simulation of speed control of DC motor has been done. We can also implement it in hardware to observe actual feasibility. Here speed control of DC motor is done for rated and below rated speed. We can also control the speed of DC motor above rated speed and this can be done by field flux control.
International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved
59
REFERENCES
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[3] Rovithakis G.A., Christodoulou M.A. “Direct adaptive regulation using dynamic neural network: Application to D.C. Motors speed control”
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[8] Veronesi M., Visioli A. “Performance assessment and retuning of PID controllers for integral processes” Journal of Process Control 20 pp261–269, 2010.
[9] Sheel S., Gupta Omhari, “Speed Control of DC Motor using PID Controller with Buck Converter as Final control Element: A comprehensive Study” submitted to be published.
