Viewgraphs on terminology and concepts of control and fuzzy logic are presented. Topics covered include: control systems; issues in the design of a control system; state space control for inverted pendulum; proportional-integral-derivative (PID) controller; fuzzy controller; and fuzzy rule processing

Aldridge, Jack

Jani, Yashvant

Lea, Robert

Weiss, Jonathan

English

NASA Technical Reports Server

TERMINOLOGY AND CONCEPTS 
OF CONTROL AND FUZZY LOGIC 
Presented at 
A Workshop on Fuzzy Control 
Huntington Beach, CA 
14 Novern ber 1990 
Dr. Jack Aldridge, MDSSC SSD (Houston) 
Dr. Robert Lea NASAIJSC 
Dr. Yashvant Jani Lincom Corp. 
Dr. Jonathan Weiss MDSSC-SSD (Houston) 
https://ntrs.nasa.gov/search.jsp?R=19930022254 2020-03-17T05:10:28+00:00Z
PURPOSES OF THIS TALK 
- MCDONNELL DOUGLflS 
Briefly review control history - how do ideas "fit together" 
1 %  Establish terminology of control theory and fuzzy logic to 
promote useful discussions 
i+~d 
Establish basic concepts in both areas for the same purpose 4 
CONTROL SYSTEMS 
- MCDONNELL DOUGLAS 
A means by which a variable quantity or a set of variable 
quantities is made to conform to a prescribed norm or to vary in a 
prescribed way 
May be operated by electrical means, mechanical means, 
hydraulic means, pneumatic means, or a combination 
2 
CmmJ~mOvrnkr 
Open Loop Control Closed Loop Control 
Servomechanism 
Input Output 
Controlled Process 
Compensator 
or Plant 
Error 
Feedback 
Processor 
- 
Physical System, 
Controlled Process - - 
CONTROL THEORY WAS FORMULATED IN THREE PHASES 1 
- MCDONNELL DOUGLRS I 
Primitive Classical 
ISSUES IN THE DESIGN OF A CONTROL SYSTEM 
-MCDONNELL DOUGLRS 
Stability and Transient Response 
Response Time or Bandwidth 
Observability 
Controllability 
Continuous or Sampled Data 
Single or Multiple Control Loops 
Optimizing or "Near-Optimal" Control 
Fixed, Adaptive, or Learning Control 
EXAMPLES: INVERTED PENDULUM 
- M C D O N N E L L  D O U G L A S  
Control Problem: 
Determine a control 
force, f, applied to the 
cart (pivot point) to keep 
pendulum at fixed angle 
STATE SPACE CONTROL FOR INVERTED PENDULUM 
- MCDONNELL DOUGLAS 
Equations of Motion 
.* 
State 
' 2  (M+rn) 2 + d o s e  8- rn Qe sine = f 
2 "  
mhosOi+mQ 8 -m&in8=0  
State S ~ a c e  Description of Dvnamical Svstern 
- 
;Lm 0 
v = &s~n I 
M + m sin 2 9  r m  sin28 ++ M + m sin 0 
= g sine(M + m) 2 W - m ~ s i n ~  - fcos 8 
a(M+ msin2 0) M + msin 2 8  M + m sin 2 0 
LINEARIZED STATE SPACE 
- MCDONNELL DOUGLAS 
DYNAMICAL SYSTEM MODEL FOR 
INVERTED PENDULUM ON A CART 
- MCDONNELL DOUGLRS 
Proportional component reduces error 
Integral component reduces steady state offset 
Derivative component anticipates and reduces overshoots 
I 
PROPORTIONAL-INTEGRAL-DERIVATIVE (PID) 
CONTROLLER 
- MCDONNELL DOUGLAS 
I 
9 
ADVANTAGES OF USING CONVENTIONAL CONTROL 
- MCDONNELL DOUGLAS 
Technology is well established 
Many control problems are well approximated by linear plants 
or can be handled with adaptive systems that perturb controller 
8 parameters 
Technology is mathematically based allowing general properties 
of controllers to be explored by a theoretical approach 
PROBLEMS WITH STATE SPACE CONTROL? 
- MCDONNELL DOUGLflS 
Model building stage is elaborate, iterative, error-prone, and 
time consuming 
A performance index that can be used for optimization must 
8 
be formulated 
Actuators may be nonlinear 
Complex equipment may be poorly described by systems of 
differential equations but may be best described from 
experimental data or heuristics (rules of thumb or experience). 
Heuristics may be part of the operating procedure and may 
be based on mental models other than the physical models 
FUZZY CONTROLLER OVERVIEW 
- MCDONNELL DOUGLAS 
Fuzzv 
Set 
-
Membership 
Functions 
DESIGNER-SUPPLIED 
INFORMATION IS UNDERLINED 
Def uzzif ier 
Techniques 
MAX 
Centroid 
IF ... THEN ... Rules 
Defuzzif ier 
X 1 
- 
2 '- 
Control 
Outputs 
IF XI is 20' 
THEN u l  is NS 
IF x l  is NS 
THEN u l  is PB 
U2 
X 3 IF x2 is Small "3 
x ( &] 4 
AND x4 is Large 
THEN u2 is Ns 
Sensor 
Inputs Fuzzifier Rule Processing 
. 
I 
N/\S/\ MISSION SUPPORT DIRECTORATE JSC 
APPROACH (CONT.) 
FUZZY PROCESSING 
MIN MAX' 
NB NM N S  ZO PS P M  PB 
INPUT . -------------. 
PHI = 4.5 lJ 1 
C 
I INPUT 
PHI DOT = 0.1 
- P i  
- 180 - 5  - 4  - 3  - 2  - 1  0 1 2 3 4 5 180 
I RULE: IF ( PHI EQ PB AND PHI DOT EQ ZO) THEN ACCELERATION IS NS MIN P1) IS APPLIED T ~ N S  FUNCTION IN ACCELERATION 
/ 
MIN MAX 
OUTPUT 
ACCEL 
I 
- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 
SPACECRAFT SOFTWARE DIVISION 
RULE BASE FOR FORCE ON INVERTED PENDULUM CART / .  1 
- MCDONNELL DOUGLAS 
Angle 
20 
Example Rule: IF Angle is PS AND Angle Rate is NS THEN Force is ZO 
A - N E f i  MISSION SUPPORT DIRECTORATE JSC 
INPUT 
PHI 
INPUT 
PHI DOT 
- 
APPROACH (CoNT.) 
FUZZY PROCESSING 
MIN MAX ' 
TWO RULES FIRE: I. IFPHI IS PB AND PHI DOT I S  PS THEN ACCEL IS  NS 
2. IFPHI IS PB AND P H I D O T  IS PM THEN ACCEL IS NM 
- 
ACCEL IS OUTPUT 
VIA CENTROID 
METHOD 
MIN MAX 
- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 
SPACECRAFT SOFTWARE DIVISION 
e- • a 
FUZZY RULE PROCESSING 
- MCDONNELL DOUGLAS 
USE MAXIMUM FOR LOGICAL OR 
IF ... THEN u is NS .3 NB NS ZO , PS PB 
IF ... THEN u is ZO .8 
IF ... THEN u is PS .I 
IF ... THEN u is PB .3 
USE MINIMUM FOR LOGICAL AND 
% 
Rule: IF x l  is NS AND x2 is ZO Other options exist for 
THEN u is PS combining logical 
connectives but these 
Facts: preserve all results 
XI is NS 0.2 from normal set theory 
x2 is ZO 0.8 => u is PS 0.2 except exclusion law: 
AANDNOTA=a 
Fu=Y b* Plwrrlng 
A 
- MCDONNELL DOUGLRS 
MAX Procedure 
Centroid Procedure 
Indexed MAX or Centroid Procedure 
Same as above except use only points > threshold value 
FUZZY CONTROLLER ADVANTAGES 
- MCDONNELL DOUGLRS 
Can exploit heuristic knowledge of operation of controlled 
systems. This includes physical intuition. 
Can accomodate small changes in system or controller 
parameters. This are the aging effect and nonlinear effects such 
as flexibility of beams 
(0 
rl 
Experience has been that these techniques seem to handle 
nonlinearity well 
Tools have been developed to assist in studying and building 
fuzzy controllers in short times 
The development of fuzzy chips has provided computationally 
capable platforms on which to build the controller, independent of 
general purpose computers used for spacecraft control 
I 
I 
! 
REMAINING ISSUES FOR FUZZY CONTROL - 
- MCDONNELL DOUGLAS 
. . 
e 
Issues such as stability, observgibility, and controllability 
raised in servomechanism and state space control are not yet in 
comparable state of developmerit. This may limit initial 
applicability to noncritical applications I 
8 Definition of membership functiqns . is arbitrary and controller 
designer dependent. \ 
Procedures for selecting membership functions and defuzzifier 
options are not firmly established in the control community 
There are limited sources for fuzzy control chips 
FC 
* a 
, 


Terminology and concepts of control and Fuzzy Logic

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