Page 1 of 8 2013-IA CC-336

A Robust Adaptive Fuzzy Controller for Drives and Transport Delayed Systems

Abdul R. Ofoli, University of Tennessee at Chattanooga

Chattanooga, TN 37403, USA, Abdul-Ofoli@utc.edu

ABSTRACT: This paper presents an adaptive-fuzzy logic

control application for different plant models. The adaptive­

fuzzy controller will automatically tune for a given plant

model with very minimal manual effort and also account for

the aging and degradation of the actuator, sensor and the plant

itself. The self-tuning controller will also take care of systems

with transport delays or dead times. The controller was tested

on different plants with sensor degradation and transport delay

issues. It was also applied to a dc machine drive for torque

control. The controller shows very interesting adaptation and

tracking results with disturbance. Different initial fuzzy rules

were tried with interesting adaptation of the rule surface. A

comparison with a classical fuzzy controller was made to

show the effectiveness of the proposed controller. A real-time

implementation of this strategy is currently in progress for

experimental verification on a DC machine drive.

Keywords: Adaptive-fuzzy controller, plant aging, actuator and sensor degradation, transport delay, and real-time implementation.

I. Introduction

Fuzzy logic control and its applications are still not

widespread as compared to conventional techniques like PI

controllers in the industrial world. Quality research in this area

needs to continue especially in this era of knowledge

revolution to take full advantage of it. Fuzzy logic uses fuzzy

values to capture the meaning of words, human reasoning and

decision making. It provides a method to encode and apply

human knowledge in a form that accurately reflects an expert

understanding of difficult and complex problems. In recent

literature, fuzzy control applications to drives and power

electronics and other general applications have been on the

rise with different adaptation techniques. This is mainly to

make it robust in the event of uncertainties and changes in the

system of interest. In [1], an adaptive membership scheme is

introduce to help learn the fuzzy inference system. In [2-6],

hybrid implementation of fuzzy scheme have been

implemented and tested including neuro-fuzzy, fuzzy-PID,

and H-infinity fuzzy control schemes. Stand-alone adaptive

fuzzy schemes applied to motor drives are reported in [7-8].

Sliding mode control with fuzzy schemes have also being

investigated in the literature sample reference is given in [9-

10]. An application to fuzzy control DC-DC converters and

power system is reported in [11-12]. In general, there has been

Bibin Patel and Nassim Khalid Cununins Inc

Columbus, IN, USA

a specific effort to design an adaptive or hybrid fuzzy scheme

for a system. This work involves the development of a robust

adaptive fuzzy control scheme that is capable of controlling

different sub-systems. In addition, it's design to adapt to aging

plant systems and sensor gain changes as the system ages. The

self-tuning adaptive-fuzzy also works well for systems with

inherent transport delay problems.

II. Fuzzy Control System - Description

In the fuzzy system, crisp inputs (error and l'J.error) are used

to determine the degree to which these inputs belong to each

of the appropriate fuzzy or membership sets during the

fuzzification process. In the Fuzzy Inference Engine, the

fuzzified inputs are applied to the antecedents of the fuzzy

rules using the fuzzy OR operator:

IlAUB(X) = max[IlA(x),IlB(X)] (1)

The results of the antecedent evaluation are them applied to

the membership functions of the consequent which in this case

a singleton was used as the membership function of the rule

consequent. This was implemented in the form:

IF x is A, OR Y is B, THEN z is k (2)

A block diagram of a basic fuzzy logic configuration system is shown in Figure 1.

----------------------------------,

, Fuzification

.... '\

Fuzzy Inference Engine

( Rule Base)

.... _---------------------------------,

Figure 1 Configuration of a basic fuzzy logic system

\ I

The membership sets used is shown in Figure 2 and the fuzzy

rules are given in Table 1.

;---1

Figure 2 Normalized membership set for both the error and l'J.error variables

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2013-IA CC-336 Page 2 of 8

There are 5 membership functions assumed for error and change in error which are Negative Big, Negative, Zero, Positive, Positive Big. The main consideration is aimed at controlling the output state of a system to a targeted reference input while making sure all other states within the system are stabilized

III. Adaptive Fuzzy Controller

The adaptive-fuzzy controller takes the current error (error), current rate of change of error (f:.error), the delayed error if

there is a transport delay (error _delay) and the delayed rate

of change of error (f:.error _delay) as inputs. The output initial

membership functions which define the control surface

according to the rules combinations are all singletons, Cj• The

singletons are modified according to the adaptive modifier

algorithm which will be described later in this section. The

overall configuration of the adaptive-fuzzy controller is

shown in Figure 3. If there is a system with transport delay

characteristics, and estimate of the total transport delay is used

in the "Transport Delay" block shown in Figure 3.

lJerror

Fuzzy Inference Engine

( R uIe 8 ase)

c::pdaffld

Adaptation

c,

Figure 3 Block Diagram of the Adaptive-Fuzzy Controller Configuration

If there is no transport delay in the system, the time for the

"Transport Delay" block is set to zero and the output of all the

membership functions becomes equal. The error and change in

error are also used in the adaptation algorithm. The

membership sets are similar to the fuzzy system shown in

Figure 2. Because of the adaption rule used, singletons were

used as the membership function of the rule consequent to

make it easier for mathematical manipulation. The initial

adaptive-fuzzy rules and control surface could be similar to

the fuzzy logic controller in Table I or it could start from an

initial value of zero for all the output singletons before

adaptation begins.

IV. Adaptation Mechanism

The adaptation system makes use of the fuzzy OR function on the antecedent results for the delayed inputs,

max[PAdela/x), PH_de/ayCX)] and also uses the actual error

and change in error. The updated control or singleton is adapted as:

C updated - C ( ) * G ( 1 :') I - i + JL Ai"Si _delay X p e + M;:C

Where G p is the adaptive learning gain and

A is the adaptive learning rate.

(3)

The final control action output which will be the final actuator

command is computed by the aggregation of all the rule

consequents including the singletons and the weighted average

of the singletons are computed: n " JL C updated

� AinBi I

U = -,-i _____ _ (4)

V. Test System #1: DC Motor Drive System

Experimental Determination of Motor Parameters

The parameters for the DC-machine used in this research was

not from a name-plate data but was experimentally determine

in the lab. An experiment was done to characterize the DC­

motor used in this paper using dSPACE platform. In this

experiment characterization of a DC-motor will be done,

which will be helpful in designing the closed loop control of

DC-motor. To detennine the DC-motor steady state

characteristics, a DC-generator, to be used as load, will be

axially coupled to the motor under test. The DC-generator will

be open-loop voltage controlled, similar to the DC-motor. The

steady-state mechanical characteristics of a DC-motor are the

dependency between the electromagnetic torque (N-m) and

the electrical speed (rad/s). Since the dependency is linear, so

will be the characteristics for the voltage range as shown in

equations in (5) and (6).

VII/otor = Ra ja + k£OJ Te = k£Ja

The equations used to characterize the steady-state are:

(5)

(6)

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R V 01(1 ) = - _0 1 + molar = ml + n o k 0 k 0

where E E

(7)

(8)

For the torque-speed characteristics, the motor voltage was

maintained constant at 35 V, 21 V, 10 V, 5 V and 3 V and the

load was adjusted to obtain motor current in the range of 0 to

5 A. The speed-torque characteristics curves obtained is

shown in Figure 4. A summary of the characteristics obtained

from analysis is shown in Table 2. To determine the friction

parameters, the motor was run under no load conditions so the

motor will have to overcome only friction (i.e. TL = 0). The

characteristic obtained is shown in Figure 5. A summary of

the steady-state characteristic obtained from the experimental

results and used in this research is shown in Table 3.

4�0,-----------------------------,

4000 _________ -----.--------->----.-. _ ... 3�0

3000

� 2�0 ----......... � 2000 --��--��--����

"C 1500 OJ OJ � 1000 ��, �� __ � ____ � __ �

500

0.09 0.54 1.01 1.53 2.01 2.53 3.11 3.50 4.10 4.55 5.00 Current (A)

�M_Speed_35V ........ M_Speed_21 V _M_Speed_10V ..... M_Speed_SV __ M_Speed_3V

Figure 4 Speed -Torque (current) plots at different motor voltage

Table 2: ke and Ra obtained for speed-torque curves Voltage m n ke

(V) (slope) (intercept) V/(rad/s) 35 -8.2528 417.54 0.0838 2 1 -9.6320 254.32 0.0826 10 -9.4632 117.58 0.0850 5 -9.0746 55.3542 0.0903 3 -10.8578 37.3542 0.0805

Dynamic Characteristics

The dynamic equations of a dc-motor are:

dOl Te = TL + TjriCtion + Bm + J --­

dt

Ra Q

0.6918 0.7953 0.8048 0.8197 0.8738

(9)

(10)

The system of two first order differential equations shows that

the DC-motor is a second order system. The two state

variables, armature current (ia) and angular speed (w), are not

independent. Therefore, the inductance (La) and the moment of

inertia U) would both contribute to the variation of each of the

two state variables. It is convenient to "isolate" the state

variables described in equations (9) and (10), thus only a fIrst­

order differential equation has to be solved for each variable.

Two sets of experiments are required to determine La and j,

while keeping the speed and the current zero respectively.

Torque vs Speed at No Load

0.2 -,----------------------------------,

0.18

0.16

0.14

5' Z 0.12 '-' � 0.1 == :: 0.08 o Eo- 0.06

0.04

0.02

6.63 61.08 152.09 304.86 Speed (rad/sec)

-Torque

415.32

Figure 5 Torque - Speed plot obtained at no-load conditions

Table 3: Summary of steady-state characteristics

m N B Tfriction (slope) (intercept) Nm/(rad/s) (Nm)

1.44*10'4 0.1194 1.44* 10-4 0.1194

Inductance Determination

To estimate the armature inductance, the motor must be held a

standstill (w = 0). If the rotor is blocked and a step voltage is

then applied to the armature terminals, the current increases

exponentially to the final value equal to va

. The slope of this Ra

exponential curve, measured at t = 0, is dependent on the

value of inductance La as given below:

d· V R Ra*O

�I = _0 _0 e-r:; dt 1=0 R L o 0

(11)

A graphical determination of the slope, at a given voltage,

would lead to the determination of the motor inductance (La).

Figure 6 shows the current waveform trajectory for a step

voltage of 5V that was used to obtain an inductance value of

0.1076 H.

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Determination of Inertia

The motor is brought to a no-load steady-state (l :; = 0) speed Wa, by disconnecting the load (TL = 0). To make

electrical torque (Te) equal to zero in the mechanical dynamics

equation (10), a complete shutdown of the motor supply is

required.

The dynamic equation will then be:

dO) 0= TL + Tfncllon + BO) + J-­dt 2.5

(12)

� I Actual Motor Current ----- Fitted line to determine slope

2

0.5

0.5 1.5

\

2 T i me (sec)

2.5 3.5 4

Figure 6 Current waveform trajectory for a step voltage of 5V with motor at standstill

Just after shutting down the system, the equation (12) can be

written and solve for J as

-(Tfrlction + BO)o) J = -----'-:---:----

( �� }=o+

(13)

By knowing (Vo, fa (0-) and graphically determining the

slope (dW)

of the speed curve at (t = 0+), the system dt t=o+ inertial can be calculated using equation (13). Figure 7 shows

the speed waveform trajectory after the system was shutdown

with speed around 450 rad/sec that was used to obtain an

inertia value of 6.6459* 10-4 kg_m2. 450

400

350

300 m � 250 = �

200 � rn 150

100

50

0 0 0.5 1.5

----- Fitted line to determ i ne slope

2 2.5 Time (sec)

3 3.5 4 4.5

Figure 7 Speed waveform trajectory after system shutdown at 450 rad/sec

VI. Test System #2: A Hydraulic System

The hydraulic system shown in Figurel is composed of a tank

of liquid of mass density rho. The tank shown in cross section

in Figure 8 is a cylindrical with bottom area A. A flow source

dumps liquid into the tank at the mass flow rate qmi(t).

Figure 8 A hydraulic system with a flow source [13]

The total mass in the tank is = rhoAh. From conservation of mass we have

dm dh dt = pA

dt = q nll - q mo

since rho and A are constants.

(14)

If the outlet is a pipe that discharges to atmospheric pressure, pa and provides a resistance to flow that is proportional to the pressure difference across its ends, then the outlet flow rate is

1 pgh qmo = "R[(pgh + Pa) - Pal = R (15)

where R is called the fluid resistance. Combining the two equations, the transfer function in equation 16 is obtained.

If(s) 1

Qmi(s) pAs + pg / R (16)

If it takes a time T for the change in input flow to reach the tank following a change in the valve opening, then T is a dead time. For specific parameters and including the transport delay, the new transfer function of equation 17 was used [13].

If(s) -Ts 2 ---= e ---

Qi(S) 5s+1 (17)

VII. Implementation and Test Results

The two test systems described in the previous sections (i.e.

the DC-motor drive system and the hydraulic system) were

used to demonstrate the significance and applicability of the

proposed controller. Several test cases were performed to

assess the performance of the proposed adaptive fuzzy

controller but for brevity, only few cases are reported for

illustration purposes. The general representation of the block

diagram of the test system with control is shown in Figure 9.

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The load or disturbance block could be a sudden change in

load or disturbance applied to the system. The plant aging is

modeled by changing specific parameters of the plant which

could vary due to aging while the sensor gain change model is

implemented as a gain change in any of the state parameters

which are read by sensors on the plant.

Controller( s) Tested: ... Fuzzy, Adaptive·Fuzzy

and PI

Output

Figure 9 General block diagram representation of the test system with control

VIII. Results for Current (Torque) Control of

DC-Motor

Fuzzy Control

The fuzzy control surface based on the rules shown in Table 1

is shown in Figure 10.

� 0.8 " '§ (f) 0.6 e § 0.4 u � N N 0.2 � LL

0.5

·0.5

Error-Dot ·1 ·1 Error

Figure 10 Fuzzy control surface

0.5

This control surface was intentionally not tuned to remove the

overshoots that occurred during a step response. Using the DC

motor system described in section V under test system 1, the

step response for the fuzzy logic controller is shown in Figure

11.

Adaptive-Fuzzy Control

An adaptive-fuzzy controller application for current control

was implemented using the fuzzy control surface as its initial

surface. The result of the step response is shown in Figure 12

with the final control surface after 10 minutes run shown on

Figure 13.

Proportional-Integral (PI) Control:

A PI controller was tune for fast response for the DC motor

current/torque control with kp gain of 0.30 and k; gain of 20.

The result of the PI controller for a step in the current is

shown in Figure 14. It shows an initial overshoot but settles

quickly within few seconds. These gains were maintained and

used for other test system for comparison purposes.

0.9 ,,-,-,-,-;====:===========]1 i i i i _I Step Input

0.8 . . . . . Ti'" T····· r···· r ---�- pe7rmanc�e of FU�ZY con�troller

0.7 ...... 'rr' , . , , . , ,

0.1

2 4 6 7 9 Time (sec)

10

Figure 11 Step response results for fuzzy controller

0.8 rl-- Step Input f------- Performance of Adaptive-Fuzzy with Fuzzy Initial Surface I

0.7 ...... : : : : : : : : : ",." i

;< :: ....•• teItte!:t � 0.4 ...... j-···r·····:·······f······;······:······�·······c ...... f····· � ::: :::::: C::::c:::r:::T:::::C:::::::::::::::::L:::r:::

0.1 . . . . . . . . . . . • ] .•••••. ; ....... l . . . . . . j . . . . . . ] . . . . . . ; ....... � ...... j .... .

2 4 i i i i i

6 Time (sec)

Figure 12 Step response results for adaptive-fuzzy

10

Using Zero Initial Surface for Adaptive-Fuzzy with Aged

system

Using a flat control surface with all singletons initialized to

zero, the adaptive-fuzzy was applied to the step and the result

obtained is shown in Figure 15 which is very identical to the

results in Figure 12. The same zero initial conditions were

used and applied to a transient input reference with the system

aged at 35 seconds of the run. The system was aged by

changing the ke and kt gain of the motor from 0.084 to 0.12

and the [mal current output multiplied by a factor of two to

mimic sensor gain changes. The initial zero flat surface used is

shown in Figure 16. The result of this transient run is shown in

Figure 17 with the [mal control surface in Figure 18. This

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2013-IA CC-336 Page 6 of 8

shows that, the adaptive-fuzzy controller is robust enough

irrespective of the initial fuzzy control surface.

"§ (f) 0.5 :;; ;;: "-i -0.5 � l� - � -, - - � �

g C � '-' a �

-1 1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.5

Error-Dot

-0.5 -1 -1

-� .... -.... -��

0.5 -0.5

Error

Figure 13 Final control surface for step response

i i i I Step Input I ------ ------:-------:------- :-- 1 ----- Performance of the PI Controller � , , , , , , , , , , ,

,

, .

, , .

, , , - - - - - - - - - - - - � - ------.-------.... ------ . ------ .. ------ .... -------.... - - - - - - � - ----,

. , ,

. ,

. , ,

. , ,

. , , ,

, . , , . , , , ,

. , ,

. , , , ,

. , ,

. , , ,

------ ------.;-------:------- :-------+------.;-------:-------:-------f------, .

, , .

, , , , . , , . , . , ,

. , ,

. , , , ,

. , ,

. , , ,

, . , , . , . , ------ ------,-------.-------.... ------T ------ .. ------.,-------r-------r-----, .

, , .

, , , , . , , . , , , ,

. , ,

. , , , ,

. , ,

. , , ,

, . , , . , . , - - - - - - - - - - - _ .. ----- - . .. - - - - _ ..... - - - - - - � - - - - - _ .. -------' . - - - - _ ..... - - - - - - � - ----, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , - - - - - - - - - - - - � - - - - - - -'- - - - - - -'- - - - - - -! - - - - - - � - - - - - - -' - - - - - - - '- - - - - - - � - ----, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

- - - - - - - - - - - - � - ------,-------,. - - - - - - � - ----- -. ------ .,-------,. - - - - - - � - ----, , , , , , , , , , , , , , , , , , , , , , , ,

, , , , , , , ,

Time (sec)

Figure 14 Step response results for PI controller

0.8 -----l Step Input r I ----- Performance of Adaptive-Fuzzy with zero initial flat surface I 0.7

�/: l: . : : . : : : 0.6 ------ -1- - - < - - - - - - " !" - -----, ------ , - - - - - - r -----,-------, ------, -----

g 0.5 - - - - - - -f - - - - � - - - - - - -l- - - - - - -l-- - - - - - t - - - - - - � - - - - - - -l - - - - - - -l- - - - - - - � -----

]i : , l l , l , l , � '-' :: :::::: t:::::L:::r:::::[::::::::::::I::::::::::::�::::::C:: � r : i i i i : : :

: :: :::::: >::::: l:::::: I:::::::::::::::::::::::::::::::::::::::::: [::::: " , " ,

° O�--L---�

2----L---�

4--�----6L---�---L---L--�

10 Time (sec)

Figure 15 Step response results for adaptive-fuzzy with zero initial flat surface

VIII. Results for Hydraulic System with

Transport Delay

The hydraulic system plant used here was discussed earlier in section VI of the paper. The main purpose was to make sure a real system is being used for this control studies. Without making any changes in any of the controllers, they were

applied to this hydraulic system which has a transport delay to see their robustness with minimal changes.

1 -,-

� u 0.5 '§ en

l '-' � -0.5

-1 1

0.5

-0.5 Error-Dot

�-� �-�� : �

�, - - !- - � - �

-1 -1

0.5

-0.5 Error

Figure 16 Adaptive-fuzzy control surface (zero initial)

1 ----Transient input ref (with aged system occuring at 35 sec) I 0_9 - - - - - - j ----- Performance of Adaptive-F uzzy with no Initial Tuning �

, , . , , , .

, 0.8 - - - - - - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - � ...... ----t , ,

. , , ,

. ,

0.7 ----------- , ----------- ,----------- ,----------- , ---------- ----------, , . , , ,

. , , ,

. , ,

- - - - - - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - � - ---------- ---------- ----------

, . . , - - - - - - - - - - - r - - - - - - - - - - - r - - - - - - - - - - - � - - - - - - - - - - - - - - - - - - - - - - � - --------, ,.

, , ,.

, , . .

, o ,

,.

,

� 0.4 -----------

r----------

r--------) ,

-----------

: ---------

0.3 -----------r-----------V ,

----------- r----------- r ---------

: .: :::::::::::t----------t:::::::::::l:::::::::::;:::::::::::;:::::::::: 00 10 30 50 20 40

Time (sec) 60

Figure 17 Transient response results for adaptive-fuzzy with zero initial flat surface

1 -,-� u m '3

en 0.5 11 ..;:

>­N N � LL .� -0.5 � ii -1

1 0.5

Error-Dot

-0.5

- ' � -��; �

� � - - :- - �

-1 -1

0.5

-0.5 Error

Figure 18 Normalized adaptive-fuzzy control surface (final)

The delay of the system was set at one second. The change

which was made a cross board was to run all the controllers at

a new slower rate of lOOms for all to account for the transport

delay. The result of the adaptive-fuzzy control is shown in

Figure 19 which managed to track the system after an initial

overshoot. The results for both the fuzzy and PI controllers are

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Page 7 of 8 2013-IA CC-336

shown in Figure 20 and Figure 21 respectively. The system

went unstable for both cases which mean that both the fuzzy

control surface and the PI gains need to be tuned.

� "EO � u 0 �

1.8 ,-----,-----,-----,----,----,-----,--,-----,----,----,

1.6

1.4

1.2

0.8

0.6

0.4

0.2

0 0

- - - - - -! - - - - - - � - - - - - - -'- - - - - - -'- - - - - - -! -- - - - -.! - - - - - - -' - - - - - - - '- - - - - - - � -----, , , . . . , , , , , . . . . , , , -- Step Input (Transport Delay System) ----- Performance of Adaptive-Fuzzy Without Re-Tuning Controller

, , , . . . , , , , , , . . . , , , ------ . - - - - - - � ------- .-------.... ------ . ------ .. ------.... -------.... - - - - - - � -----, , . . . . , , , , . , . . . , , , , , . . . . , , , , , . . . . , , . , , , . . . , , , , , . . . . , , , ------ i ------,-------,-------,------- i ------ -; -------,-------,------- , -----, , . . . . , , , , . . . . : I�'\ : : : : ------t!---\-i-------l-------�------t------i------�-------�------�-----, , . . . . , , , -- ---i------j-------!-------�------j------j------�-------,------,-----

- - - - -1 ------ � -- - - - - -1-- - - - - -�-------� ------ �-- - - - - -� - - - - - - -�- - - - - - - � -----: : : : : : : : : : ( , , . . . . . . . -- --rT------'-------.-------r-------T------'------ .,-------r-------r-----

J i i i i i i i i i 10 20 30 4 0 50 60 70

Time (sec) 80 90 100

Figure 19 Step response results for adaptive-fuzzy without re-

1.8

1.6

1.4

1.2 � � u 0 0.8 � 0.6

0.4

0.2

0 0

tuning controller

1 --Step Input (Transport Oelay System) 1 ------1 ----- Performance of Fuzzy Without Re-Tuning Control Surface � , , . , , . . , , . . . . . . , , , , , , , . . , , , . . . . . . , , , ------ T------,-------,-------r------- T------,------.,-------r-------r-----

•••••• :f� •••••• f\t •••• if\ •• I •• I� •••• I[i ••••• :: :: t:::::\::t'::::::t:J:: t::: \: u::::::\::;/::::::\ j J , • \ • • . l t . \. J , '\ J. " , - - - -j� - - - - - - � - - :��: - -�-- - - - - -� �\�-- - - � - - - - - -1�- - - - - �- - - - -��:� - - - - - - � - -�

; : : : : : : : : : 10 20 30 4 0 50 60 70

Time (sec) 80 90 100

Figure 20 Step response results for fuzzy without re-tuning control surface

IX. Conclusion

An adaptive fuzzy logic controller which will automatically

tune for a given plant model with very minimal manual effort

have been proposed in this paper. The controller can adapt for

the aging and degradation of the actuator, sensor and the plant

itself. Many test cases have been shown to show the

effectiveness of the controller in regard to the minimal tuning

effort needed. Some of these cases include starting from a zero

flat control surface or using a working control surface. A

transient reference input was also tested with aging of the

plant and sensor gain change with good control results for the

adaptive controller. The adaptive-fuzzy controller was finally

tested with a hydraulic system having transport delay with the

controller adapting favorably without any re-tuning while

other control techniques show instabilities which needed

tuning. In general, the adaptive-fuzzy controller is robust

enough to provide considerable control performance over a

wide range of operating conditions. A real-time

implementation of this control strategy is in progress for

experimental verification on a DC machine drive.

1.8 ,-----,-----,-----,----,----,----,-----,----.----,----, , , , ,

1.6 ------ , ---- - - < -------,-------:------- , ------ , -------:-------,------- f -----, , : 1 Step Input (Transport Oelay System) I' 1A ------I--I --�-- Pe�orman�e of PI

,Withou� Re-Tu�ing Ga:ns ---r-----

1.2 - - - - - - i ------j -- - - - - -i-------� - - - - - - i ------j--- - - - j-------�- - - - - - � -----� : : : : : : : : :

1 ::::: -,�\. :: -,t,l ]: :nr-: :;"::: -,(LT,erC I}, :: -,N : :nr-:tl\,:: -,.(\ J'\ 0.8 , : " ': ( , , \ ' : ' , ': ; \ . , , '( : ' :' , ,: \ : • � 0.6 t: \: �: 1. J \.: : � J \ : : l ,I: \ � : � : l. � � �: � :

-- -1 1-\f --\(--�\:1---\f-r �r-v---\f--\j-i \(--\Jj---'J f- '\J-OA -- - � - t------ � -------:-------:------- t ------ �-------:-------:-- - - - - - � -----! 1 i 1 i i 1 i 1 i

0.2 -- -:--t------� - - - - - - -1-------� ------t ------�------�-------�------� -----! : : : : : : : : :

° 0��1�0--�2� 0--�3� 0---4� 0--�50�� 60�� 70�� 8�0 --�9� 0--�100 Time (sec)

Figure 21 Step response results for the PI without re-tuning the PI gains

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