2. Contents:
Introduction
Literature survey
Two quadrant DC Motor Drive
Transfer function of Subsystem
Symmetric optimum method
Design of current controller
Design of speed controller
Simulation Results
Conclusion
References
2
3. Introduction:
The dc machines are becoming more and more useful in
applications like electric vehicle, weak power used battery
system, the electric traction in the multi-machine systems,
etc.
There are 3 types of dc motors: self excited, permanent
magnet and separately excited dc motor.
Control of Separately Excited dc motor (SEDC) is a bit
easier since field is excited externally.
3
4. Continued..
Principle of Speed control:
The voltage equation of simple DC motor is given by,
where
Therefore,
4
Speed Can be controlled by,
• Varying supply voltage
• By varying flux & varying
current through field winding
• Varying armature current &
armature resistance.
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Continued..
The Speed of Separately excided dc motors can be
controlled by two methods:
1. First is by keeping the field excitation constant and by
controlling the armature current that is supplied by
power electronics converter.
2. Second is by field weakening where the field current is
controlled in order to increase voltage across
armature hence increase the speed.
6. 6
Literature Survey
The transfer function of conventional current controller is of 4th order
system and the simplification is difficult for higher order systems.
Thus order of transfer functions is necessary for simplification of the
system.
There are many types of order reduction methods been employed by
researchers:
1. Symmetric optimum method: The design of control loop
starts from the innermost loop and proceeds to the slowest
outer loop[1]
2. Routh approximation method: Approximating a high-order
linear system by a lower order system with most important
property being the reservation of stability[2]
3. Truncation method: This method do not make use of any
stability criterion but always lead to the stable reduced order
models for a stable system[3]
8. 8
DC Motor and load system:
• The DC machine contains an
inner loop due to induced emf.
• The inner current loop will cross
this back emf loop, creating a
complexity in development of model.
• Thus the transfer function
between speed and voltage is split
into two cascaded transfer function,
first between speed and armature
current and then between armature
current and reference input voltage.
Transfer function of Subsystem
9. 9
Transfer function of Subsystem
Converter:
The converter can be considered as a black box with
certain gain and phase delay for modelling and use in
control studies. The converter transfer function:
Current and Speed Controllers:
The current and speed controllers are PI type. The
transfer function is given as:
Current Controller:
Speed Controller:
10. 10
Transfer function of Subsystem
Current feedback:
• No filter is required for current loop.
• The gain of the current feedback is denoted by Hc.
Speed feedback:
Most high performance systems use a dc tacho-generator and the
filter required is low pass type with a time constant less than 10ms.
The transfer function of the speed feedback filter is
11. 11
Symmetric optimum method
• Symmetric optimum method is used for designing the control loop.
• The design of control loop starts from the innermost loop and
proceeds to the slowest outer loop.
• The gain and time constants of only one controller at a time are
solved, instead of solving for the gain and time constants of all
controllers simultaneously.
• The performance of the outer loop is dependent on the inner loop,
therefore the tuning of the inner loop has to precede the design
and tuning of the outer loop.
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Design of current controller:
Loop gain:
This is 4th order system.
Symmetric optimum method
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Design of current controller:
Since Tm is in the order of seconds, we can assume
Thus,
Where
Selecting Tc = T2, The loop gain reduces to 2nd order
system:
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Design of current controller:
To design the speed control loop, the second order model of the
current loop is replaced with an approximate first order model.
where
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Design of speed controller:
Since Tm is in the order of seconds, we can assume
Approximating ,
where
The closed loop transfer function
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Design of speed controller:
By taking the magnitude and solving we get,
Substituting for Ks and Ts ,
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EXAMPLE:
To design a speed controlled dc motor. The motor
parameters and ratings are as follows:
220 V, 8.3 A, 1470 rpm, Ra=4 ohms, J=0.0607 Kg-m2,
La = 0.072 H, Bt = 0.0869 N-m/rad/sec,
Kb = 1.26 V/rad/sec.
The converter is supplied from 230V,3-phase ac at 50 Hz.
The converter is linear, and its maximum control input
voltage is ±10 V. The tacho-generator has the transfer
function.
Simulation Results
23. Conclusion:
Literature survey is conducted on the different types of order reduction
methods which is been developed for reducing higher order transfer
functions to lower order.
The Conventional motor drive system is been analyzed and transfer
functions are derived.
Brief introduction to the symmetrical optimization method for reducing
the order of transfer function motor drive is studied.
Overall transfer function of the motor drive is designed using symmetric
optimum method.
The conventional motor drive and the reduced order are simulated using
Simulink and the results are found to be same.
The motor drive control with and without current loop is simulated and
was found that the control loop without a current loop has slower
response.
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24. Reference:
[1] K.Ramesh, K.Ayyar, Dr.A.Nirmalkumar, Dr.G.Gurusamy, “Design of
Current Controller for Two Quadrant DC Motor Drive by Using Model
Order Reduction Technique”, International Journal of Computer
Science and Information Security, Vol. 7, No. 1, 2010.
[2] M.F. Hutton and B. Friedland, “Routh approximations for reducing
order linear time invariant systems”, IEEE Trans. on Auto. Control,
Vol.20, pp. 329-337, 1975.
[3] Y. Shamash, “Truncation method of reduction: a viable alternative”,
Electronics Letters, Vol.17, pp. 97-99, 1981.
[4] Ramu Krishnan, “Electric Motor Drives: Modeling, Analysis, and
Control”, published by Prentice Hall, 2001
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