A FUZZY LOGIC BASED MULTIPLE REFERENCE MODEL ADAPTIVE CONTROL (MRMAC) By Sukumar Kamalasadan, Adel A Ghandakly Khalid S Al-Olimat Dept. of Electrical Eng.

A FUZZY LOGIC BASED MULTIPLE REFERENCE MODEL ADAPTIVE

CONTROL (MRMAC)

By

Sukumar Kamalasadan, Adel A Ghandakly Khalid S Al-Olimat

Dept. of Electrical Eng. and Computer Sci., Dept. of Electrical and Computer Eng., The University of Toledo, Toledo, OH Ohio Northern University, Ada, OH

16th International Conference on Computer Applications in Industry and Engineering (CAINE-2003)Sponsored by

International Society for Computers and Their Applications(ISCA)

11th Nov 2003

Abstract

• Proposing A Fuzzy Scheme for switching Multiple Reference Models within the MRAC framework

– Following a rule base, the scheme effectively monitors drastic changes in plant operating conditions

– Reference Model switching is performed every time instant based on the plant auxiliary measurements

• The proposed scheme is computationally feasible and efficient

• It can be performed online and is well suitable for multimodal systems

• It provides an interactive multiple model environment with soft switching

• The proposed scheme is applied to an example system with distributed model parameters to show its effectiveness

• Control of Multi Modal Systems (s.a Aircraft, Robotic Arm) is difficult as the system changes its operating mode arbitrarily

Controller Properties:• It should be dynamic in nature• Efficiently respond to the system changes• Keeps track of uncertainties• Accordingly, generates appropriate control

• The Classical MRAC Framework

• Our Multiple Reference Model Adaptive Controller (MRMAC) Framework– Select a set of Reference Models suitable for the system at different

modes– Modes can include normal parametric variations , external disturbance or

both – Depending on certain schemes best suitable Reference Model at each

time instant is switched and control action is carried out

Introduction

• Heuristic based Reference Model generation• Performs switching of the Reference Model at each

time instant with respect to the plant variation• Provides a smooth change in the functional relation

between the two• Process is accomplished keeping track of the plant

auxiliary measurements• Main idea is to change the Reference Model so that it

improves the overall performance in the form of perfect tracking

Our Proposed Fuzzy MRMAC Approach

The MRMAC Concept

Multi Modal Domain – Let the system be characterized by ‘n’ Reference Models – Let these Reference Models fits in the parametric space ‘S’– ‘n’ Reference Models can be thought of representation of

‘n’ subspaces in the predefined domain ‘N’– Suppose the plant change is fully captured by these

reference models pertaining to the domain ‘N’– If any one reference model can describe the ideal plant

characteristic fully at any instant - Subspace is called “Hard Partitioned”

– Real system often exhibits transition from one subspace to another

The MRMAC Concept

− Predefined subspaces or modes switching fully from one to another is not advisable

− Need arise to smoothly change the reference model defining a trajectory movement along with the plant dynamics in order to effectively control the plant

− Effective along the imaginary boundaries of the subspace where hard switching from one reference model to another can deteriorate the system performance

− Heurstic based Multiple Reference Model Adaptive Control performs better when compared to a single reference model adaptive control

• A set of predefined Reference Models with suitable structure which models the plant for a specific domain of interest

• An effective switching scheme, which smoothly provides transition between these Reference Models keeping track of the plant change

• A robust adaptive control scheme, which tunes and provides control at each reference model subspace

The main Components of

MRMAC

• Objective– Control of Complex systems which is affine , “ Multi

Modal” and shows sudden parametric ‘Jumps’

• Features– Heuristic Based Multiple Reference Model Adaptive

Controller– Mitigating the issue related to the computational

complexities inherent in existing mathematical methods.

– An interacting individual models due to soft switching unlike hard switching algorithms

The proposed SchemeObjective and Features

• Determination of the Multiple Reference Models

• Developing a switching mechanism to switch these Reference Models online based on plant auxiliary measurements.

• Use a stable Direct Model Reference Adaptive Control (MRAC) approach

The Design Approach

Overall Scheme

:

Ref. Model 1

Ref. Model 2

Ref. Model n

Command Signal

Control Signal

Aux. Measurements

yRegulator Parameters

ErrorFuzzy Logic Switching Scheme (FLSS)

Output

+

Regulator Plant

Adjustment Mechanism

-

yR

An example Investigation

• A second order Test System is used for investigation under three mode changes

• The Test System : 1/(s2+3s-10) • Mode 1 :- 1/(s2+30s-10) • Mode 2 :- 1/(s2+3s-20) • Mode 3 :- 1/(s2+9s-30) • The RM that worked best with the original Test System :-• 5/(s2+10s+25) • The RM that worked best during transition between each

mode :- • 5/(s2+4s+4)

Time T <40 T<70 T<100

Plant Structure 1/(s2+30s-10) 1/(s2+3s-20) 1/(s2+9s-30)

 Best RM 5/(s2+4s+4) 5/(s2+4s+4) 5/(s2+4s+4)

Results comparing output tracking error

Expanding the Test Domain

• Three cases are generated each with three modes of plant change

• Table below shows the plant Multiple Modal changes for these cases

Time T <40 T<70 T<100

Plant Modes 1/(s2+30s-10) 1/(s2+3s-20) 1/(s2+9s-30)

 Plant Modes 1/(s2+9s-30) 1/(s2+30s-10) 1/(s2+3s-30)

Plant Modes 1/(s2+18s-10) 1/(s2+24s-10) 1/(s2+9s-30)

Case I

Case II

Case III

An example Fuzzy Logic Scheme

• A fuzzy system knowledge base is created for complete operating domain selecting the appropriate best RM’s

• Proposed fuzzy logic switching scheme has two inputs, two outputs and nine rules

• The rule base for the case study consists of three input linguistic terms in the form of Small(S), Medium(M) and Large (L)

• The input values are taken directly as plant parameter values

• In physical process these linguistic inputs will be the plant auxiliary measurements

An example Fuzzy Logic Scheme

• The output values are reference model parametric changes directly

• There are nine rules which generates two output values

• Min Operation implication method and centroid deffuzzification method has been employed to generated crisp values

• Table below shows the rule basea0/a1(Output1) Small Medium Large

Small Medium VLarge VLargeMedium Medium Large MediumLarge Medium Large Large

a0/a1(Output2) Small Medium LargeSmall Medium Large MediumMedium Small Small MediumLarge Medium Small Small

Input Output Mapping and

Overall Fuzzy Scheme

Input and Output Membership functions

Simulation Results:Case 1

• In this case system modes are changed at different time instants as in Table below

• Fuzzy Logic switching of the RM was performed online at every time instant

• Table below shows the plant modes and fuzzy RM structure• Output error between controller with the best single RM ( the

one shown before) and fuzzified RM is compared

Time T <40 T<70 T<100

Plant Structure 1/(s2+30s-10) 1/(s2+3s-20) 1/(s2+9s-30)

Reference Structure By FLSS

5/(s2+3.51s+1.74) 5/(s2+4.46s+4.11) 5/(s2+7.23s+4.95)

Simulation Results:Case 1

Simulation Results:Case 2

• In this case system modes are changed at different time instants as in Table below

• Fuzzy Logic switching of the RM was performed online at every time instant

• Table below shows the plant modes and fuzzy RM structure• Output error between controller with the best single RM ( the

one shown before) and fuzzified RM is compared

Time T <40 T<70 T<100

Plant Structure 1/(s2+9s-30) 1/(s2+30s-10) 1/(s2+3s-30)

Reference Structure By FLSS

5/(s2+7.23s+4.95) 5/(s2+3.51s+1.74) 5/(s2+5.57s+6.32)

Simulation Results: Case 2

Simulation Results:Case 3

• In this case system modes are changed at different time instants as in Table

• Fuzzy Logic switching of the RM was performed online at every time instant

• Table shows the plant modes and fuzzy RM structure• Output error between controller with the best single RM ( the

one shown before) and fuzzified RM is compared

Time T <40 T<70 T<100

Plant Structure 1/(s2+18s-20) 1/(s2+24s-10) 1/(s2+9s-30)

Reference Structure By FLSS

5/(s2+4.62s+4.93) 5/(s2+3.51s+1.74) 5/(s2+7.23s+4.94)

Simulation Results: Case 3

Concluding Remarks

• A Multiple Reference Model Adaptive Control scheme with online Fuzzy Switching is proposed for plants with multimodal changes

• The scheme is very effective and computationally efficient for reference model switching

• Proposed scheme provides ‘soft' switching of the reference models, especially at the modal boundaries

• The scheme can be used for scheduled switching in which certain auxiliary measurements are monitored to keep track of unforeseen changes in the plant operating mode

• With the help of additional learning strategy the rule based switching can be modified online thus expanding the operating range

• The scheme can be effectively used as an Intelligent Controller for highly dynamic and functionally uncertain systems such as aircraft control

Multi Modal Domain

Predefined Domain ‘N’

Subspace‘b’

Subspace‘a’

…….

::

Subspace‘n’

• Develops a Control Law looking at the Input and Output of the Plant

• Updates the Control law using an Adaptive Mechanism

• Use a reference model to effectively model the dynamics and forces the plant to follow that model

MRAC Structure

Reference Model

Adjustment Mechanism

Regulator Plant

Control Processor

Command Signal

Control Signal

y Output

error

ym

+

- regulator Parameters