International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
February 2017, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
Nonlinear Compensation Empyoing Matrix Converter with DTC Controller Khalaf S.
Gaied1.
Ziad H.
Salih2.
Ahmed R.
Ajel3.
Mehdi J.
Marie4 College of Engineering.
Tikrit University.
Iraq College of Petroleom and Mineral Engineering.
Tikrit University.
Iraq Institute of Technology.
Baghdad.
Iraq Al-Zawraa state company.
Ministry of Industry.
Iraq
Article Info
ABSTRACT
Article history:
This paper describes a nonlinear harmful speed and torque controller for fourth order induction motor model.
The investigation of optimality and cost function for that base on estimation of Hammerstein-Wiener model with the compensated mathematical model.
The matrix converter with direct torque control combination is efficient way to get better performance specifications in the industry.
The MC and the DTC advantages are combined together.
The reduction of complexity and cost of DC link in the DTC since it has no capacitors in the circuit.
However, the controlling torque is a big problem it in DTC because of high ripple torque production which results in vibrations response in the operation of the IM as it has no PID to control the torque The combination of MC with DTC is applied to reduce the fluctuation in the output torque and minimize the steady state error.
This paper presents the simulation analysis of induction machine drives using Maltlab/Simulink toolbox R2012a.
Design of constant switching frequency MCDTC drive,stability investigation and fault protection as well as controllability and observability with minimum steady state error has been carried out which proved the effectiveness of the proposed technique.
Received Sep 10, 2016 Revised Jan 7, 2016 Accepted Jan 21, 2017 Keyword:
Direct torque control Fault diagnosis Matrix converter Nonlinear compensation Space vector modulation Copyright A 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Khalaf S.
Gaied.
Electrical Engineering Department.
Tirit University.
Tikrit state, 9647703057076.
Iraq.
Email: gaeidkhalaf@gmail.
com, salim_hazim2000@siswa.
NOMENCLATURES
ADRC
ASD
DTC
DTCIM
DSC
FPE
MCDTC
Auto Disturbance Rejection Controller Adjustable Speed Drive Direct Torque Control Direct Torque Control Induction Motor Direct Self Control Final Predicted Error Matrix Converter Matrix Converter with Direct Torque Control Induction Motor Proportional Integral Rotor Resistance Vop Vip Journal homepage: http://iaesjournal.
com/online/index.
php/IJECE Stator Inductance Rotor Inductance Mutual Inductance Stator Current Rotor Current Stator Voltage Electromotive Force Vector Sampling Period Output Voltage Vector Input Voltage Vector.
ISSN: 2088-8708
INTRODUCTION
In industry life all systems are nonlinear, to make the investigation.
nalysis and desig.
, most of these systems considered as linear.
DTC and control of non-linear levels in the systems are considered the most important techniques for achieving high performance in AC machines .
The induction motors (IM) plays an important role.
in the industry due to their low cost and operational reliability .
Adjustable speed drives (ASD.
are frequently used in many applications, such as air conditioning, elevators, electrical vehicles, ventilation, pumps, fans, heating, robotics .
In 1984.
Takahashi developed a new technique for the torque control of IM which is one kind of variable speed drives named as Direct Torque Control (DTC) .
The principle is emulate both flux and torque as in the DC machines by the orientation control of the magnetic field.
The DTC configuration for direct MC has been presented in .
In a DTCIM drive, a decoupled control of torque and flux can be achieved by two independent control loops .
This configuration play vital role in the industry due many reasons like ability to adjust input power factor, no need to DC link capacitor, ensure sinusoidal waveforms for the input and output and power flow control in the forward and backward directions.
Comprehensive researches studies on direct MC with DTC .
The available literature on DTC drives too are mainly confined to performance enhancement in terms of torque ripples.
Since the steady state as well as dynamic performance of a DTC drive is greatly affected by the flux control loop which in turn depends upon flux estimation algorithm .
Nonlinear robust controller for MC fed IMD in which a nonlinear robust ADRC is applied to the MC fed IM drive system, taking the place of PI controller .
Fuzzy logic controller of multilevel inverter, the SVM presented in .
In .
the inverter voltage vector selected from the switching table is applied for the time interval needed by the torque to reach the upper limit or lower limit of the band, where the time interval is calculated from a suitable modelling of the torque dynamics.
AC-DC-AC sparse direct power converter introduced in .
Control of a two stage direct power converter with a single voltage sensor mounted in the intermediary circuit presented in .
The DTC can be divided into two types, either DSC or SVM.
DTCSVM for IM driven by MC using a parameter estimation strategy done by .
The switching table has many drawbacks such as variable switching frequency due to hysteresis bands of both torque and flux as well as the change of speed motor.
According to this variation in switching frequency, uncontrolled small region will be generated especially in the beginning of operation of induction motor.
The main drawbacks of the DTC system are the variable inverter switching frequency and high torque output ripple due to usage of hysteresis based comparators to control the output torque .
To obtain good solution for that.
SVM with DTC and MC has been used.
The stability is one of the most important demands in the control system after being subjected to a disturbance .
The MC can be used in the compressors, fans .
, mixers, general pumps or heat pumps and escalator drive system .
In this paper, a combination of fixed switching frequency DTC with MC scheme is presented, which developed to minimize the steady state error of input torque due highly torque noise in the DTC scheme that should be suppressed.
DTC BACKGROUND
DTC can achieve field orientation without feedback, using motor theory to calculate the motor It is said to use the fastest digital signal processing hard-ware available and a more advanced mathematical understanding of how motors work .
Flux Controller Reference flux Phase currents Flux and torque Flux selector Look up table Torque Controller Phase voltages Reference torque Transistor Figure 1.
Principle of the DTC The DTC technique principle is shown in the Figure 1 can be illustrated as follow: At the first step, the phase currents and voltages of the system are measured.
The outcome of forwarding such values to the IJECE Vol.
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flux and torque estimator will be the actual flux and torque of the system.
The estimated torque is com-pared with their reference values in three levels torque hysteresis controller.
At same time, the flux is compared with the reference flux values in two levels flux hysteresis controller.
In order to construct the transistor control signal, the outputs of the stator flux and torque controllers further to the flux selector are used as inputs of the DTC switching look up table.
The transistors control signals which are divided into nine different sections are used for controlling the three levels MC, as can be shown in the Figure 2.
Figure 2.
Simulink Implementation of the Three Levels MC .
The internal connection of each level shown above will as in Figure 3.
Figure 3.
Simulink Implementation of the First Level The details information of each block shown in Figure 3 will be as in Figure 4.
Figure 4.
Details Connection of each Block shown in Figure 3 The general selection table for the DTC, being .
which is the sector number can be shown in Table 1.
Table 1.
General Selection Table s sector K
Flux
Increase Decrease Torque Increase Vk 1
Vk 2
Decrease V000
V111
Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 DTC zero sequence (V000 or V.
vectors are used to maintain the torque constant and not including during the switching period.
The switching table in DTC allows selecting the vector position to apply to the MC according to the DC of the stator flux and the electromagnetic torque as can be shown in Table 2.
From Table 1, one can notice that the switching frequency of the IGBTs used in this scheme is not constant.
If we control the tolerance bands, the average switching frequency can be kept at its reference value, hence the ripple current and torque will be minimized .
Table 2.
DTC switching Table dI= 1
dI= -1
dT= 1
dT= 0
dT= -1
dT= 1
dT= 0
dT= -1
Sector
V4 V5
V0 V7
V2 V3
V5 V6
V7 V0
V1 V2
The MCDTC proposed algorithm can be shown in Figure 5.
Figure 5.
The Proposed Fixed Frequency DTC Scheme using MC
MATRIX CONVERTER
A device which converts AC input supply to the required variable AC supply as output without any intermediate conversion process whereas in case of Inverter which converts AC - DC - AC which takes more extra components as diode rectifiers, filters, charge-up circuit but not needed those in case of MC .
device which converts AC input supply to the required variable AC supply as output without any intermediate conversion process whereas in case of Inverter which converts AC - DC - AC which takes more extra components as diode rectifiers, filters, charge-up circuit but not needed those in case of MC.
The Eupec Economac matrix module with nine back-to-back IGBT switches can be seen in Figure 6.
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Figure 6.
The Eupec Economac Matrix Module The advantages of the MC compared to conventional inverter types are as follows:
Waveforms of both Input and output are very clear .
Minimal higher order harmonics are obtained Capability of sub harmonics omitting Capability of bi-directional energy flow It has no DC link capacitors Control of input power factor can be performed easily The disadvantages of the MC are as follows:
Maximum efficiency cannot be obtained in all cases The conventional AC-AC has fewer components compared to the MC Each bi-directional switch should have its arrangement Sensitive to input voltage system No monolithic bi-directional switches exist The system consists of a 3-phase MC constructed from 9 back-to-back IGBT switches.
The MC is supplied with three phase source and drives a static resistive load.
The switching algorithm is based on SVM described earlier which considers the MC as a rectifier and inverter connected via a DC link with no energy Indirect SVM allows direct control of input current and output voltage and hence allows the power factor of the source to be controlled.
The switching algorithm utilizes a symmetric switching sequence mentioned before.
First of all the Simulink implementation of the MC is carried out.
MC consists of nine bidirectional sectors with reverse blocking capability, arranged as three sets of three so that any of the three input phases can be connected to any of the three output lines.
A bi-directional 18 diodes is used for blocking the voltage in MC .
The inversion matrix sequence of the SVM when the voltage mod input to generate .
1-v2-v7- v.
with the switching pattern is constructed as in the Figure 7.
Figure 7.
MCSVM Symmetric Switching in the Voltage Mod Input In the first position .
degree, the torque will be decreased while the flux will be increased.
the positions .
or (-120- (-.
) there is a flux ambiguity, in the position (-180- (-.
) the torque and Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 the flux will be decreased and last position .
the torque will be increase while the flux will be There are two position between.
-(-.
) are not used because the torque will increased or decreased in the same sector depending on the position if it's in the position of 30 or( -.
The symmetric sequence unit used the current mod as the input to generate .
1-v2-v.
also used.
SVM symmetric sequence unit for generation of v1_v2_v7_v8 sequence can be implemented using Matlab/Simulink as in Figure 8.
Figure 8.
SVM Symmetric Sequence Unit of the above Figure An IM can be described in the stationary frame by the following flux and voltage equations.
A s A L s i s A Lm i r A r A L m i s A Lm i r dA s .
dA r A jA rA r v s A Rs i s A 0 A Rr i r A The stator flux variation can be expressed as:
AEA s A .
s A Rs is )t sp A es t sp AA vs t sp Figure 9.
Switching Signal Construction IJECE Vol.
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To generate the control signal, the MC gates can be constructed from two lookup tables.
First one when the magnitude of the flux equal one and the other one when the flux is equal to minus one.
The combinations from 1 to 9 which are the sectors .
0-v1-v2-v3-v4-v5-v6 -v7-v.
are used as a gate signal of the IGBT transistor as can be shown in the Figure 9.
The first 6 states can be constructed from the current mode .
R) and the other 6 state as constructed from the voltage mode circuit .
The combinations of these 12 signals are used to construct the SVM used to control the MC.
Where in g is the output angle in the SVM rectification system to generate left .
and right .
R) axis of the sector when the voltage and current mode acts as the inputs to the circuits.
MC SWITHING SEQUENCE
The MC can be used as one of the following.
MC applicable as a cyclo-converter.
MC applicable as a cyclo inverter.
MC applicable as a Dual Converter, rectifier and inverter .
The control requirement of the switches of MC through the duty cycle depends on the average output voltages to construct the required sinusoidal frequency and magnitude of the three phase voltage .
The MC switching generation signal combination with the SVM rectification sequence can be shown in Figure 10.
curr mod m od SVM Rectif sym seq matrix converter switching m od volt mod SVM Rectif sym seq Figure 10.
MC switching Generation Signal The reduction of harmonics in the input power supply can be obtained by MC compared with conventional inverter as well as there is cost reduction .
The SVM modulation of the proposed algorithm, required to measure any line voltages.
Then.
Vi/p and I i/p are calculated as:
V 2 i / p A 4 (V 2 ab A V 2 bc A VabVbc ) Ai / p A tan A1 ( AVbc / 3Vab A 1 / 3Vbc The ratio between input and the output voltages is calculated as Rv A V 2o / p V 2i / p The switching function of any IGBT switch can be expressed as in .
Where K= {A.
C} is labelled input phase and j= .
, b, .
is labelled the output phase.
The condition of the switching function can be expressed by the following relationship:
S AJ A S BJ A S CJ A 1
Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 Under these constrains, a 3y3 MC has been implemented with 27possible switching states.
Let dKj .
be the duty cycle of switch SKj, defined as:
d KJ .
) A t KJ / t sampling & 0 A d KJ A 1 The low frequency of MC can be obtained by:
Ed Aa .
) E
) A Ed Ab .
) EEd Ac .
) d Ba .
) d Bb .
) d Bc .
) d Ca .
) E
d Cb .
) E d Cc .
)EE .
The Simulink implementation of duty cycle unit can be shown in Figure 11.
pi/180 deg_mag 5/0.
d1 d2 d1_d2_d0 Trigger Figure 11.
Simulink Implementation of Duty Cycle Calculation d1 _ d 2A .
os(AO ) A (A / 3 A AO ) sin( 0.
5 / 0.
866 ))* | v | d0 A 1 A Eud _d .
The low-frequency component of the output phase voltage as in .
Vop .
) A D.
Vi / p .
) .
The low frequency component of the input current as in .
I ip .
) A DT .
I op .
) .
The torque can be affected directly by the stator current as well as number of poles, mutual inductance and rotor inductance as in .
Te A p( m )(A dr i qs A A qr i ds ) .
The SVM technique is one of the most important modulations used for the DMC due to the advantages of this technique like the reduction of total harmonic distortion and the controlling the duty cycle The SVM rectifier system switching sequence can be implemented using two states current and voltage stages to yield the MC switching and hence the gates signals of the IGBTs of the MC as can be seen in the Figure 10.
The input current modulator and the voltage modulator are used for controlling of gates signals in efficient way.
The DTC with MC proposed technique depends completely on the best choice of the switching mechanism to get better steady state error of both torque and flux compared to their references.
The matric configuration switching technique used in this method can be illustrated in Table 2.
Simulink implementation of hysteresis controllers of the torque and flux can be shown in Figure 12.
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T orque* dT e/2 T orque H_T e -dT e/2 NOR Convert Flux* H_phi dPhi Flux Flux_est Figure 12.
Simulink Implementation of the Torque and Flux Hysteresis Controllers The Simulink implementation of voltage in alpha and beta coordinate can be shown in Figure 13.
1 De mux Vabc sqrt.
Valpha sqrt.
Vbe ta sqrt.
/2 sqrt.
/2 Figure 13.
Simulink Implementation of Alpha & Beta Voltage Components SIMULATION RESULTS To investigate the proposed algorithm, the Simulink program has been used first to model the IM.
MC.
DTC and speed controller.
A nonlinearity compensation strategy has been developed to make better the speed control performance in all operation regions.
The simulation has been carried out assuming that the sampling period is 20e-6 sec and ideal switching devices, 0.
8 Wb flux reference.
The results of the DTC control simulation are shown in the following figures.
The MCDTC technique is simulated with Simulink to investigate the performance of the proposed control scheme.
Figure 14 shows the speed command and the speed tracking which is completely coincided when the speed command is changed from .
RPM then increased and setteled with 1500 RPM.
actual speed reference speed Speed(RPM) Time.
Figure 14.
Speed Reference and Actual Speed Response Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 The triangular reference torque compared to the actual torque to investigate the error that will be high frequency triangular waveform.
Figure 15 shows the actual torque without constant switching The variable switching frequency in the basic DTC is due to the variation of the time taken for the torque error to achieve the upper and lower hysteresis bands.
The dynamic performances of the proposed MCDTC control method are tested for a variable torque command.
The waveform and the steady state error slopes are highly dependent on operating conditions.
Consequently, the torque ripple will remain high, even with small hysteresis band.
The fluctuation in the DC voltage during the operation period can be shown in Figure 16.
The torque ripples which are generated due to the operation of hysteresis controller are reduced by using the proposed control method as can be shown in Figure 17.
Torque(N.
Time.
Figure 15.
Actual .
and Reference Torque Dynamic without Constant Frequency DTC DC voltage(Vol.
Time.
Figure 16.
DC Voltage without Constant Frequency DTC torque(N.
Time.
Figure 17.
Actual and Reference Torques with Proposed DTC IJECE Vol.
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Stator current with proposed method can be shown in Figure 18.
Stator current Stator Current(Am.
Time.
Figure 18.
Stator Current with the Proposed DTC Scheme The stator current in the Figure 18 shows acceptable results of the proposed strategy.
The switching frequency of the IGBTs is 6 kHz and can be realized up to 20 kHz.
To ensure better design of the proposed algorithm, 20 samples residues autocorrelation and cross correlation for both input and input combinations proves good results as can be shown in Figure 19.
Autocorrelation of residuals for output .
Cross corr for input .
and output .
resids Samples Figure 19.
Autocorrelation and Cross Correlation Residuals The transfer function of system from torque to the speed as in .
00024 s A3 A 2.
744e A 6s A2 A 5.
49e A 9s A 5.
901e A 12 s A 4 A 0.
0055 s A3 A 1.
3e A 5s A 2 A 2.
74 s A 2.
34e A 11 The speed controller PI controller transfer function with zero delay time designed as in .
GPID A 1 A Tp s * exp( ATd .
K p A A0.
Td A 0.
T p A 87.
Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 The minimum difference between the input and the output has been tested through many fitting methods to ensure better performance in the IM as can be shown in Figure 20.
Measured minus simulated model output Difference between(Measured &Simulate.
Sixth Fitting Method Fourth Fitting Method Second Fitting Method Fifth Fitting Method Third Fitting Method First Fitting Method Time.
Figure 20.
Nonlineary .
Test of the Output Regions The values of of Figure 20 fitting method can be listed in the Table 3 using identification Matlab/Simulink toolboxes .
Table 3.
Fitting Method to get the best Output Model The Fitting Method First Fitting method SecondFitting method Third Fitting method Fourth Fitting method Fifth Fitting method Sixth Fitting method The value Name Nlarx1 N4s4 N4s1 Arx441 Nlarx2 Nonlinear torque and speed harmful residual cross correlation can be shown in Figure 21.
Autocorrelation of residuals for speedharm Cross corr for nonlinear torque and speed arm resids Samples Figure 21.
Nonlinear Torque and Speed Harmful Residual Cross Correlation IJECE Vol.
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Estimation of the nonlinearity of the output before and after applying the proposed algorithm will be listed in the Table 4.
Table 4.
Nonlinearity Information with and without Proposed Algorithm
without constant switching Frequency Fit (%) FPE
Loss Function
With constant switching frequency Fit (%) FPE
Loss Function
918E-4
872E-4
The state space model of the system will be 4th order.
Matlab instruction is used to find whether the system is controllable, observable or not as in .
& .
Co A cntrb ( A.
B ) .
E0.
0028 - 0.
1175 - 0.
E- 0.
3307 - 7.
4653 - 1.
Co = E E 0.
2165 - 5.
E - 0.
8181 - 0.
6350 - 0.
Obsv A obsv( A.
C ) .
E1.
0e 03 * E E 1.
6710 - 0.
0875 - 0.
O bsv = E 0.
0000 - 0.
0450 - 0.
E - 0.
1190 - 0.
0226 - 0.
E - 0.
0000 - 0.
1766 - 0.
With rank of 4, the system is completely controllable and observable.
The stability test determines if all roots of the input polynomial lie inside the unit circle.
Implemented using the Schur-Cohn algorithm can be shown in Figure 22.
The output is containing the value 1 or 0.
The value 1 indicates that the system is stable while the value 0 indicates that the system is unstable.
Time .
Figure 22.
Stability Test according to Schur-Cohn Algorithm
MODEL IMOROVMENT
To insure best controller design.
Estimation of Hammerstein-Wiener model before and after controller design can be used as can be shown in Table 5 and Table 6.
The block diagram represents the structure of a Hammerstein-Wiener model can be shown in Figure 23.
Because acts on the output port of the linear block, this function is called the output nonlinearity.
system contains several inputs and outputs, you must define the functions f and h for each input and output Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 U.
Input W.
Linear B/f Y.
Figure 23.
Block diagram of Hammerstein-Wiener where: w.
= f.
) is a nonlinear function transforming input data u.
has the same dimension as u.
= (B/F)w.
is a linear transfer function.
has the same dimension as y.
where B and F are similar to polynomials in the linear Output-Error model.
For ny outputs and nu inputs, the linear block is a transfer function matrix containing entries:
linear Block A B j ,i .
/ F j ,i .
where j = 1,2,.
,ny and i = 1,2,.
,nu.
= h.
) is a nonlinear function that maps the output of the linear block to the system output.
and x.
are internal variables that define the input and output of the linear block, respectively.
Because f acts on the input port of the linear block.
Table 5.
Estimation of Hammerstein-Wiener model at the beginning Table 6.
Estimation of Hammerstein-Wiener model after design the compensation Itr Cost Step size Optimality Step Optimality Bisection The nonlinearity level in the circuit of IM can be shown as in Figure 24.
Linear Block Nonlinearity Value nlhw1:pwlinear Input to nonlinearity at input 'u1' Figure 24.
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The continuous canonical state space model of the given system will be as in the following form:
X .
A Ax A Bu A Ke y A Cx A Du A e With the following values:
AAE
E2.
7e A 5 0.
E0.
E4.
8e A 5E E .
C A Au1
BAE
E0.
E0.
0Ay E0.
E0.
D A Au0Ay .
K A E E0.
E0.
Another evidence to show the model improvement is the power distribution along with the operation of the system as shown in Figure 25.
Power Spectrum power spectrum Power spectrum Frequency .
Figure 25.
Power spectrum distribution There are no sensitive parameters during the IM running with higher speeds, but at low speeds the stator flux estimation becomes so important and critical due to error in stator resistance property .
, .
FAULT DIAGNOSIS
The control of electrical machines, vehicle, space exploration faulty is very important in all industrial applications.
The fault tolerant control princible are needed with these applications according to safety of operation of system operation.
There are difference in operation and control between faulty and healthy machines.
The danger of significant oscillations in faulted machine such as speed and torque oscillation is the main cause for damage of the machines .
The IM model is constructed with the following assumptions .
The air gap is of constant No eccentricity effect.
The system works under balanced load .
Pure simusoidal input source.
Nonlinear Compensation Empyoing Matrix Converter with DTC Controller (Khalaf S.
Gaie.
A ISSN: 2088-8708 Shutting down the IM operation is another improvement especially when the motor performance is In Figure 26, both motor and the controller works presicely untle 0.
6 sec after that we simulate a fault between .
sec to investigated the protection circuit which is reacts in a very good manner and stoped the operation to avoid the motor damage.
protection period when the motor in bad performaance Speed(RPM) Time.
Figure 26.
protection circuit activation CONCLUSIONS Hammerstein-Wiener is proposed as identified optimization model.
DTC and MC modelling and simulation have been carried out.
The proposed algorithm tested to ensure better performance specifications.
DTCMC converter is used for supplying the IM.
Minimizations of the steady state error of the torque with lowest final predicted error are obtained.
Stability has been tested according to Schur-Cohn algorithm.
The proposed algorithm with the constant switching frequency helped to design controllable, observable states of the given system.
Protection circuit isn extra improvement for the proposed scheme which is not mentioned in detail in this paper.
State space transfer function and design of the PI controller investigated with identification facilities of the Matlab/Simulink as well as the torque, the speed and current waveforms proves the effectiveness of the control scheme.
REFERENCES