INTERNATIONAL JOURNAL FOR RESEARCH IN EMERGING SCIENCE AND TECHNOLOGY, VOLUME-4, ISSUE-2, FEB-2017 E-ISSN: 2349-7610
Study and Analysis of Controller for PMSM
A.Mahendran
1, S.Neelan
2and T.Ilansezhian
31
A.Mahendran, / Electrical & Electronics Engineering, IFET College of Engineering, India
11
[email protected]
2
S.Neelan /Electrical & Electronics Engineering, IFET College of Engineering, India
22
[email protected]
3
T.Ilansezhian /Electrical & Electronics Engineering, IFET College of Engineering, India
33
[email protected]
ABSTRACT
In this paper the control statergy of Permanent Magnet Synchronous Motor (PMSM) is been analysed through two types of Controller. The speed of permanent magnet synchronous motor taken as objective for this control statergy[1]. Rectifier circuits and Pulse width modulation and inverter-motor modelling satisfies to biuld the design. An vital role takes part in desingning and tunning the PI and Fuzzy Controller to analyse the performance of PMSM
Index Term—
Permanent magnet synchronous motor (PMSM), Control, PI and Fuzzy controller
.1. INTRODUCTION
Permanent Magnet Synchronous Motors generally have the same operating and performance characteristics as synchronous machines in general operation at synchronous speed, a single (or) poly-phase source of AC supplying the armature windings, a power limit above which operation at synchronous speed is unstable, reversible power flow etc. A permanent magnet machine can have a configuration almost identical to that of the conventional synchronous machine with absence of slip rings and a field winding.
The previous works on synchronous machine speed control have simplified the control problem neglecting the dynamics of the AC/DC rectifier, i.e. focusing only on the set ‗DC/AC inverter-motor‘. This reduced system has been dealt with using several control strategies ranging from simple techniques. A control strategy that ignores the presence of the AC/DC rectifier suffers at least from two drawbacks.
First, the controller design relies on the assumption that the DC voltage is perfectly regulated; the point is that perfect regulation of the rectifier output voltage cannot be ensured ignoring the rectifier load, which is nothing other than the set
‗DC/AC inverter-motor‘. The second drawback lies in the entire negligence of the PFC requirement.
In the present work, a new control strategy is developed that simultaneously deals with both involved sub- systems, i.e. the AC/DC inverter and the combination ‗DC/AC inverter-motor‘. The new control strategy is featured by its multi-loops nature and its robustness against parametric uncertainty.
2. DC TO AC RECTIFIER
For three-phase AC, six diodes are used. Typically there are three pairs of diodes, each pair, though, is not the same kind of double diode that would be used for a full wave single-phase rectifier. Instead the pairs are in series (anode to cathode).
Typically, commercially available double diodes have four terminals so the user can configure them as single-phase split supply use, for half a bridge, or for three-phase use. Most devices that generate alternating current (such devices are called alternators) generate three-phase AC. For example, an automobile alternator has six diodes inside it to function as a full-wave rectifier for battery charging applications.
The average and root-mean-square output voltages of an ideal single phase full wave rectifier can be calculated as:
For an ideal three-phase full wave rectifier, the average output voltage is,
Where,
Vdc, Vav → the average or DC output voltage Vpeak → the peak value of half wave
Vrms → the root mean square value of output voltage π = 3.14159
α → firing angle of the thyristor (equal to zero if diodes are used to perform rectification).
3. CONTROLLER DESIGN & MODELLING
A PI Controller (proportional-integral controller) is a special case of the PID controller in which the derivative (D) of the error is not used.
The controller output is given by
Where,
Δ → error or deviation of actual measured value (PV) from the set-point (SP).
Δ = SP − PV
A PI controller can be modelled easily in software such as Simulink using a "flow chart" box involving Laplace operators:
Where,
G = KP = proportional gain G / τ = KI = integral gain
Setting a value for G is often a trade-off between decreasing overshoot and increasing settling time. The lack of derivative action may make the system steadier in the steady state in the case of noisy data. This is because derivative action is more sensitive to higher-frequency terms in the inputs.
Without derivative action, a PI-controlled system is less responsive to real (non-noise) and relatively fast alterations in state and so the system will be slower to reach set-point and slower to respond to perturbations than a well-tuned PID system may be.
3.1 FUZZY CONTROLLER:
The fuzzy logic controller has two input variables. the first is speed error e(k) and the second is change of speed error ce(k) . At the same time, change in reference phase current iq*(k) is the output Δiq*(k).
Structure of fuzzy logic controller
Internal structure of fuzzy controller
All paragraphs must be indented. All paragraphs must be justified.
3.2 MODELLING:
a) AC/DC rectifier modeling:
The power supply net is connected to an H-bridge converter which consists of four IGBT‘s with anti-parallel diodes for bidirectional power flow mode. This is expected to accomplish two main tasks: (i) providing a constant DC link voltage and (ii) providing an almost unitary power factor.
Applying Kirchoff‘s laws, this subsystem is described by the following set of differential equations:
i) die / dt = Ve / Li – (1/Li) * S Vdc ii) dVdc / dt = (1/2C) * S ie – (1/2C) * is Where,
ie → current in inductor L1 Vdc → voltage in capacitor 2C is → inverter input current
b) Inverter-motor modeling:
This kind of modeling is generally performed [10] in the dq-coordinate. The inverter is featured by the fact that the stator d- and q- voltage can be controlled independently. To the end, these voltages are expressed in function of the corresponding control action:
i) dɷ / dt = - F ɷ / j + 3KMiq / 2j – TL / j
ii) diq / dt = -R iq / L – ρ ɷ id – KM ɷ / L + Vq / L iii) did / dt = -R id / L + ρ ɷ iq + Vd / L
Where,
Vd, Vq → averaged stator voltage in dq- coordinate
The state space equations obtained up to now are put together to get a state-space model of the whole system including the AC/DC/AC converters combined with the synchronous motor.
For convenience, the whole model is rewritten here for future reference:
i) dx1 / dt = Ve / Le – u1 x2 / L1 ii) dx2 / dt = u1 x1 / 2C – is / 2C
iii) dx3 / dt = -F x3 / j + 3KM x4 / 2j – TL / j iv) dx4 = -R x4 / L – ρ x3 x5 – KM x3 / L + u2 x2 / L v) dx5 = -R x5 / L + ρ x3 x4 + u3 x2 / L
Where,
x1 = ie ;x2 = Vdc ;x3 = ɷ ;x4 = iq ;x5 = id
and these represents the average values over the cutting periods
u1, u2, u3 → control signals
The following equations which is been used to model the sub block of the system DQ/ABC,
F(u)= u(1)*cos[u(4)]+u(2)*sin(u(4))+u(3)
F(u)= u(1)*cos[u(4)]-2*pi/3]+u(2)*sin[u(4)-2*pi/3]+u(3) F(u)= u(1)*cos[u(4)]+2*pi/3]+u(2)*sin[u(4)+2*pi/3]+u(3)
F(u) =
4. SIMULINK RESULT & CONCLUSION
Speed control of PMSM using fuzzy controller
Speed control of PMSM using PI controller
Speed VS Time (PI controller)
Speed VS Time (fuzzy controller)
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ACKNOWLEDGEMENTS
The author‘s are thankful to Management trustee Mr.V.Raja Chairman ,Mr.A.Mohamed Ilyas Vice chairman and Dr.G.Mahendran Principal, Prof S.Matilda Dean Academics, Prof J.Asha Dean Placement/ Student Affairs P.Pugazhendiran HoD/R&D, and C.Sundhar HoD/EEE, IFET College of Engineering, Villupuram for providing necessary facilities for the preparation of the paper. Last but not least I thank my parents for their love and blessings throughout my work.
AUTHOR’S BIBLIOGRAPHY
A.Mahendran received B.E. degree Electronics & Instrumentation Engineering and M.E. degree in Control and Instrumentation. He is currently working at IFET college of Engineering as Senior Assistant Professor/EEE. He attended two international and one national conference and published Six international journals. His main area of interest are control systems, nonlinear system and instrumentation. He is a life member in ISTE.
Mr.T.Ilansezhian has obtained B.Tech.
(EEE) from Pondicherry University, Pondicherry in 2007, M.Tech. (Electrical Drives and Control), Pondicherry Engineering College, Pondicherry university in 2010. He has published 2 papers in International Journals and 6 papers in International and National Conferences. His area of interest include Control System, FACTS controllers and Power Electronics. Currently He is an Associate Professor in the Department of Electrical and Electronics Engineering,
Mr.S.Neelan received B.E. degree Electrical & Electronics Engineering (2009) and M.E. degree in Power Systems (2012) from Annamalai University. He is currently working at IFET college of Engineering as Assistant Professor/EEE. He has published 3
and National Conferences. His area of interest include Power Systems, Renewable Enrergy. He is currently Senior Assistant Professor in the Department of Electrical and Electronics Engineering.
