optimization techniques analysis on various optimization ... · optimization techniques references...

RBEI/EHV2 | 3/28/2016

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Optimization Techniques

Analysis on various optimization techniques for selecting gain

parameters in FOC of an E-drive

Presented by:

RAJA SEKHAR KAMMALA(RBEI/EHV2)

SATHISH LAKSHMANAN(RBEI/EHV2)

MEHER ANUSHA VANAPALLI (NITC, Intern at RBEI)

RBEI/EHV2 | 3/28/2016



1. Introduction

2. Problem Statement

3. Various Optimization techniques considered

1. Pattern Search

2. Genetic Algorithm

3. Simulated Annealing

4. Error Criteria and Objective function

5. Results

1. Comparison of optimization techniques

2. Graphs and data generated.

6. Conclusion

RBEI/EHV2 | 3/28/2016



1. Introduction

Field Oriented Control (FOC) is commonly used for controlling the electrical machines like PMSM and Induction machines etc.,

which are majorly used in Electric and Hybrid Vehicles

For optimal performance of the algorithm (FOC) or any PID based controller it is required that the controller is tuned to its best

parameters over the entire operating range of the electrical machine.

Several conventional methods (Ziegler-Nichols) to optimize the current control parameters in FOC, (or tuning any PID controller)

were highly unsatisfactory in terms of large overshoot and steady state error, because of manual involvement in selecting the

initial points and tuning them.

The paper compares different optimization techniques like Pattern Search, Genetic Algorithm and Simulated Annealing

algorithms and the best possible results are presented.

RBEI/EHV2 | 3/28/2016



2. Problem Statement

P.U Speed-Torque characteristics of 83kW PMSM machine used in FIAT500e are shown below.

In FOC control of above Permanent Magnet Synchronous Motor (PMSM), finding tuned Controller Gain parameters are required

to achieve high performance.

Each working point(In Speed torque characteristics of E-Machine) shown below, will have unique Kp and Ki values.

Torq

ue[N

m]

Speed[rpm]Base

speed

1P.U

1P.U

P.U N-T characteristics of PMSM

RBEI/EHV2 | 3/28/2016



2. Problem Statement (Contd..)

To find optimized values (which gives minimum overshoot and steady state error) of gain parameters as a function of speed and

torque, pattern search algorithm with error criteria has been used.

Pattern search failed to provide tuned Kp and Ki at working points above base speed and in few cases even at below base

speed.

Torq

ue[N

m]

Speed[rpm]Base

speed

P.U N-T characteristics of PMSM

To overcome above problem, investigations on

different optimization techniques has been done.

RBEI/EHV2 | 3/28/2016



MATLAB Implementation: FOC of PMSM

Fig.1 FOC of PMSMImplemented in MATLAB using

Simscape .ssc scripting

Implemented in MATLAB using

SimElectronic toolboxImplemented in MATLAB using Simulink modelling,

Interpreted MATLAB Functions and Optimization tool box

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3. Various Optimization Techniques considered

1. Pattern Search

2. Genetic Algorithm

3. Simulated Annealing

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4. Error Criteria and Objective function:

The performance indices taken for optimization are:

ISE (Integral Square Error)

ITSE (Integral time Square Error)

Overshoot

Tolerance band

The above performance indices are used to minimize error between desired and actual id, iq and torque values. The

summation of above performance indices results to an objective function.

0.01s 0.3s0.2s

ITSE

ISE

Steady_Statetolerance

C(t)Overshoot

Objective function = Minimum ( ISE_Id + ISE_Iq + ISE_Torque + ITSE_Id + ITSE_Iq + ITSE_Torque )

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ISE (Integral Square Error):

where, ‘e’ corresponds to error.

It penalizes both positive and negative values of the error

Gives more weight to larger deviations

Suitable for control circuits of which one calls weak overshoot

Here only error is considered and therefore no weight is given to time span of error.

ITSE( Integral time squared error):

For time-weighted quality criteria, the duration of the standard deviation is taken into account.

By multiplying with the time, Minor variations which occur relatively later can be recognized

This will be responsible for Less settling time and faster reduction in oscillations.

Tolerance band:

If actual response lies in between this tolerance band, that solution can be accepted.

dtteISE

0

2

dttteITSE

0

2

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Overshoot Function:

Overshoot is the maximum peak value of the response curve measured from the desired response of the system.

Here Cpeak = first peak value of the response

C(∞) = Steady state response of the system

Steady State Function:

It defines the allowable ripple in the system with respect to desired during steadystate

100)(

)(%

C

CCpeakMp

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5. Results : Comparison of Pattern Search, Genetic Algorithm and simulated Annealing

Kp Ki Peak Overshoot (%) Ripple(%) Settling time

(Secs)

Convergence

time (Secs)

Working Point ‘a’ : Speed 0.19P.U and Torque 0.9P.U (Below Base Speed)

PS 1.5624 329.2 2.22 2.58 0.55 4.0781e+03

GA 1.8156 399 0.56 1.78 0.04 1.544e+04

SA 1.4596 588.4 1.24 1.42 0.02 1.55e+05

Working Point ‘b’ : Speed 0.38P.U and Torque 0.9P.U (Base Speed)

PS Not

converged

Not

converged

GA 1.784 387 1.78 1.96 0.05 2.3773e+04

SA 1.9912 201 1.24 2.04 0.08 1.67e+05

Working Point ‘c’ : Speed 0.5P.U and Torque 0.578P.U (Above Base Speed)

PS Not

converged

Not

converged

GA 2.6148 730.4 1.38 3.32 0.035 2.2509e+04

SA 2.7732 579.8 1.04 3.46 0.04 1.5375e+05

For comparing results of above

specified optimization techniques,

three working points are

considered(Below base speed,

base speed and above base

speed ).

Torq

ue[N

m]

Speed[rpm]Base

speed

Below Base

speed

Above Base

speed

Fig.10 Speed torque char. Of PMSM

RBEI/EHV2 | 3/28/2016



5. Results at above base speed with PS, GA and SA:

Pattern search failed to converge as

limitation in ‘tolfun’ reached. Objective

function value = 1e6.

Objective function output and Kp ,Ki values are shown below for all the three techniques at above base speed.

Pattern Search Genetic Algorithm

Objective function output reaches to 6.3e-

6. Thus the output obtained are optimized.

Kp= 0.4P.U and Ki = 0.36P.U

Simulated Annealing

Objective function output reaches to 6.3e-

6. Thus the output obtained are optimized.

Kp= 0.44P.U and Ki = 0.29P.U

(a)(c)(b)

Fig.11 Results for (a)Pattern search (b)Genetic Algorithm (c)Simulated Annealing

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5. Results: Torque waveform in transient and steady state region:

As pattern search outputs are

not converging, an overshoot

is observed.

Fig.12 Torque waveform at speed:0.5P.U and torque:0.578P.U

Torque( Nm)

t(seconds)

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6. Conclusion

Initial point selection plays a vital role in pattern search output convergence. If a better initial point is chosen,

Pattern Search converges fast.

At working point greater than base speed, GA and SA are giving good results compared to PS, where SA

takes more time to give a converged result.

The performance of SA can be improved with ‘hybrid function’.

Goal Achieved:

GA and SA algorithms of optimization tool box can be used to find out optimized values of current control

parameters in FOC control of 83kW PMSM for FIAT 500e machine for speeds above base speed.

These values can be used in calibration stage directly. This methodology decreases lot of time in finding the

tuned parameters.

RBEI/EHV2 | 3/28/2016



References

Vikrant Vishal, Vineet Kumar, K.P.S. Rana, Puneet Mishra “Comparative Study of Some Optimization Techniques Applied

to DC Motor Control” IEEE International Advance Computing Conference (IACC). 2014.

P.Tripura, Y.S.Kishore Babu, Y.R.Tagore “Space Vector Pulse Width Modulation Schemes for Two-Level Voltage Source

Inverter” ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011.

Bin Wu, High-Power Converters and AC Drives. IEEE Press, 2006.

Tomy Sebastian ,Gordon R. Slemon and M.A. rcahman “Modelling of Permanent Magnet Synchronous Motors” IEEE

Transactions on Magnetics, vol. mag-22, no. 5, September 1986

Simscape language Guide and Global optimization tool box guide(MATLAB)

Bosch internal material.

THANK YOU

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