a dissertation proposal presentation by sukumar kamalasadan

A New Generation of Adaptive Control: An Intelligent Supervisory Loop

Approach

A Dissertation Proposal PresentationBy

Sukumar Kamalasadan

Department of Electrical Engineering and Computer Science,University of Toledo,

30th April 2003

Dynamic Systems

Operates in Real time Specifies Performance Quality Regardless of External Disturbance

Complex Dynamic Systems Uncertainties: Functional and Parametric Time Varying and/or nonlinear elements

The Control Challenge, A Practical Matter :

Practical Systems are mostly Nonlinear and Shows some degree of Uncertainty

Advances in technology led to highly complex processes, to be controlled with tight specifications and high level of autonomy

Example: Fighter Aircrafts

Practical Approaches to the Control Design Problem

Systems that can be modeled “Adequately” with stationary Linear Models: Fixed Parameters (Stationary) Controllers Designed off

line. Mostly used for Linear Time Invariant Systems

Systems that CANNOT be modeled “Satisfactorily” with stationary Linear Models: Adaptive Controllers (STR and MRAC)

Sophistication Level # 1 Intelligent Adaptive Controllers (A New Generation)

Sophistication Level # 2Which Implies Certain Levels of

Learning and Adaptation

Research Motivation

Investigate possibilities of some Intelligence based solutions to a major structural problem that exists in the two “conventional” Adaptive

Control techniques (MRAC & STR ):

The Problem: The Designer’s A priori Choices, such as the choice of a

“MODEL” as required in either of the two Schemes Inability to Control functionally nonlinear and Changing

systems

Intelligent Adaptive Control

What is Intelligent Control ? Controls complex uncertain systems within stringent

specification Features

Ability to Learn: Ability to modify behavior when condition changes

Ability to Adapt: Ability to handle uncertainty by continuously estimating the relevant unknown knowledge

Ability to deal with Complex Systems : Characterized by nonlinear dynamics and multiple mode of operation

Autonomous in Nature: Ability to deal with uncertainty all by itself without human intervention

Intelligent Adaptive Control : Constituents

Adaptive Control Deals with linear or nonlinear parametric uncertain Systems Needs detailed prior knowledge of the systems to be controlled Have the ability to adapt

Artificial Intelligence (AI) Techniques Neural Networks

Ability to learn either offline or online Adjusts the parametric values allow the network to learn

Fuzzy Systems Ability to fuzzify a complex system in terms of linguistic rules Can avoid dealing with complex mathematical models Create the “long term memory” or learning behavior Reduce the uncertainty in dealing with models

Intelligent Adaptive Control : Applications

Objective

Control of Complex systems which is affine but shows “ Multi Modal” and Sudden parametric ‘Jumps’

Control of Nonlinear Systems which shows “Functional Uncertainty”

Control of Nonlinear Systems which shows “Functional Uncertainty” and “Multi Modal”

Statement of Dissertation Objectives

Theoretical Design and Development of Three Intelligent Adaptive Control Schemes

Develop an F-16 Aircraft Model in MATLAB for Investigation and Application

ClassificationI. Development of the F-16 Aircraft MATLAB ModelII. Fuzzy Switching Multiple Reference Model Adaptive Co

ntrol SchemeIII. Neural Network Adaptive Control SchemeIV. Neuro-Fuzzy Adaptive Control Scheme

Current Status of Dissertation

Development of a 6 Degree of Freedom (6 DOF) dynamic F16 Aircraft Model in MATLAB and SIMULINK

Development of a Fuzzy Switching Multiple Reference Model Adaptive Controller

Development of a Neural Network Adaptive Controller

Development of Neuro-Fuzzy Adaptive Controller Overall Dissertation Status

Concluding Remarks

Three Intelligent Adaptive Control schemes are proposed Objective is to control a class of multimodal nonlinear systems

which deals with function and/or parametric uncertainty Application systems which shows changes influenced by

external or internal disturbance A nonlinear Aircraft Model is developed to simulate as an

appropriate application system, and to investigate and verify the effectiveness of schemes

Preliminary Simulation Results appear to be promising

Typical Stationary Controller

Regulator Plant Control Signal

Command

Signal

y

Output

Regulator

Parameters

Control processor

A stationary (Fixed Parameter) Controller is

designed ( Off Line ) For

The Plant as represented

by a Stationary (Fixed Parameter) M odel

Self Tuning Regulator (STR) Scheme

Design Calculations

Parameter Estimation

Regulator Plant Control Signal

Command Signal

Control Processor

y Output

Regulator Parameters

Model Reference Adaptive Control (MRAC) Scheme

Reference Model

Adjustment Mechanism

Regulator Plant

Control Processor

Command Signal Control

Signal y Output

error

ym

+

- regulator Parameters

Development of the F-16 Aircraft MATLAB Model

Developing the Building Blocks Developing the Algorithm in MATLAB includin

g the subroutine functions and the main equations of motions

Testing with certain developed Trim conditions Developing the SIMULINK Model

F-16 Aircraft Body System Axes and Variables

AerodynamicModel

Engine ModelAtmosphericModel

6DOF EquationsOf Motion

Control deflections

Actuator Modeling

F-16 Aircraft Model Building Blocks

Development of the F-16 Aircraft MATLAB Model

Computing Air dataOutputs: - Mach number, Dynamic Pressure Inputs: -Velocity,

Altitude

Aerodynamic look-up table and coefficient buildupOutputs: - Aerodynamic Force (Cxt, Cyt, Czt) & Moments (Cnt, Clt, Cmt)

coefficientsInputs: -Control Variables (elev, ail, rdr) and (alpha, beta)

Computing Engine Model Outputs: - Engine ThrustInputs: -Power, Altitude, Mach Number

State EquationsForce Equations Derivative, Inputs: -Moment Rates (P, Q, R), Velocity (UVW), Kinematics (Phi, Theta)

and Aerodynamic Force coefficientsOutputs: - Vt, Alpha and Beta Derivatives

Kinematic Equations Derivative, Inputs: -Moment Rates (P, Q and R), Kinematics (Phi and Theta)Outputs: - Phi, Theta and Psi Derivaties

Moments Equations Derivative, Inputs: -Moment Rates (P, Q, R), Aerodynamic Moment Coefficient (Clt,Cmt.Cnt) and Inertia ConstantsOutputs: - Moments Derivatives

Navigation Equations DerivativeInputs: -Moment Rates (P, Q, R), Aerodynamic Moment Coefficient (Clt,Cmt.Cnt) and Inertia Constants

Outputs: - Moments Derivatives

Control Vector

Development of Steady State Trim Conditions

Trim Conditions are Developed based on a Simplex Routine Table Below Shows the Trim conditions for five cases

Conditions

Variables Nominal Xcg=0.38C Xcg=0.38C

VT(ft/sec) 502.0 5020 502.0 502.0 502.0

(rad) 0.03691 0.03936 0.03544 0.2485 0.3006

(rad) -4.0E-9 4.1E-9 3.1E-8 4.8E-4 4.1E-5

(rad) 0 0 0 1.367 0

(rad) 0.03691 0.03936 0.03544 0.05185 0.3006

P(rad/sec) 0 0 0 -0.01555 0

Q(rad/sec) 0 0 0 0.2934 0.3000

R(rad/sec) 0 0 0 0.06071 0

Thtl(0-1) 0.1385 0.1485 0.1325 0.8499 1.023

El(deg) -0.7588 -1.931 -0.05590 -6.256 -7.082

Ail(deg) -1.2E-7 -7.0E-8 -5.1E-7 0.09891 -6.2E-4

Rdr(deg) -6.2E-7 8.3E-7 -4.3E-6 -0.4218 0.01655

Reference Models

(90S+287)(S3+20.87S2+115S+28)

(110S+287)(S3+20.87S2+115S

+287)

(235S+4163)(S3+40S2+608S+416

3)

(10S+287)(S3+20.87S2+115S+287

(132S+287)(S3+20.87S2+115S+287

sec/3.0 rad

sec/3.0 rad

CX cg 3.0

CX cg 3.0

Developed SIMULINK model of F16 Aircraft

Proposed Scheme I

Scheme Outline Developing the Model Reference Control Law Development of Reference Models for each

operating modes Testing the operation by manually switching the

Reference Model Developing the Fuzzy Logic Scheme depending on

the System Testing overall system with the Dynamic Fuzzy

Switching Scheme

Proposed Scheme I

:

Ref. Model 1

Ref. Model 2

Ref. Model n

Command Signal

Control Signal

Aux. Inputs

y

Regulator Parameters

ErrorFuzzy Logic Switching Scheme (FLSS)

Output

+

Regulator Plant


-

MRAC Structure

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

Proposed Scheme II

Scheme Outline Design of the Dynamic Radial Basis Neural

Network (RBFNN) Development of overall scheme linking the R

BFNN control with Adaptive Control Testing the Scheme on a Functionally

Nonlinear System

Proposed Scheme II

++

Usl

-

+

+

Umr

Unn

em

ym

yp

Neural Network Controller

Nonlinear ProcessMRAC Controller


Reference Model

Neural Network

Features of Proposed Neural Network

Radial Basis Function Neural Network

Features

Dynamic in Nature Centers, Radius and Distance adapt with time looking at input vector

Grows accordingly Starts with three nodes and grows

depending on functional complexity

Learns Online RBFNN weights adjust to correct the Output and Reference Error

RBFNN Structure Consists of Nodes in Input layer Nodes basically have two elements : Center and Radius Consists of a basis function which is a Gaussian Function The output is the summation of each functions times the weights

Proposed Scheme II(Nonlinear Functional Uncertain System)

Highlights RBFNN

Center Grows depending on new Inputs Moves close to Input Set

Radius : Changes for each center addition Weights: Adapts Depending on the Error

MRAC Stable Direct Model Reference Framework

Sliding Mode Gain and Rate Increase Reduces Network Approximation Error Reduces Parametric Drift especially in the Boundary Region

Proposed Scheme III

Scheme Outline Design of the RBFNN Control Design of Fuzzy Logic Scheme depending on the

System Development of the Reference Model Integrating overall scheme Testing the system on a Functionally Nonlinear

Parametrically Uncertain System

Proposed Scheme III

+

+ +

Usl

-

+Umr

Unn

em

ym

yp

Neural Network Controller

Nonlinear ProcessMRAC Controller


Reference Model ‘1’

Reference Model ‘2’

Reference Model ‘n’

::

Fuzzy Logic SwitchingAuxiliary Inputs

Reference Input

Desired Inputs

Flight Control System

Sensor Measurements

Pilot Command

Reference Measurements

Controller Output(Thtl,Rdr,Elev,Ail)

Proposed Scheme III(Nonlinear Complex System)

Neural NetworkFlight Pattern

Model

Adaptive Control


Fuzzy Switching

Proposed Scheme III(Nonlinear Complex System)

Status: Nonlinear F16 6DOF Model in MATLAB and SIMULINK

Developed the Building Blocks of the Aircraft Model

Developed 6 DOF nonlinear Aircraft Model Developed Steady State Trim Conditions Algorithmic Development in MATLAB has

completed Developed Graphical Equivalent in the

SIMULINK

Status : Scheme 1 and Simulation Results

Problem Formulation has been established Derived a Stable Model Reference Adaptive Law Developed a Fuzzy Logic Switching Scheme Developed a Multiple Reference Model suitable

for all ‘modes’ Simulation Results for a Linear ‘Jump’ System Simulation Results of the Pitch Rate Control of

F16 Aircraft

Status: Scheme 2 and Simulation Results

Problem Formulation has been established Developed a RBFNN Architecture which is

dynamic in nature Derived a Stable Adaptive Law and developed an

overall system Simulation Results to control a Nonlinear Process Application of the Developed scheme to control

F16 aircraft Dynamics is yet to be accomplished

Status : Scheme 3 and Simulation Results Problem Formulation has been established Developed an dynamic RBFNN Architecture Development of a Fuzzy Logic Switching Scheme

is yet to be accomplished Development of a Multiple Reference Model

suitable for all ‘modes’ is yet to be done Integration of Overall Scheme is yet to be done Application to a Nonlinear Process and F16

Dynamics Control is yet to be done

Proposed Scheme I(Linear Parametric “Jump” System)

Proposed Scheme I( Linear Parametric “Jump” System)

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)

Time T <40 T<70 T<100



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

Time T <40 T<70 T<100



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

I

II

III

Proposed Scheme I( Linear parametric “Jump” System)

Proposed Scheme I( Pitch Rate Control of F-16 Aircraft)


Single Link Robotic Manipulator with Payload

Neural Network Inversion

Desired Position

Desired Other States

Actual Position


Time

Posi

tion

Tra

ject

ory

Overall Dissertation Status

ProposedTasks Proposed Sub Tasks Status

Development of the Building Blocks of the Aircraft Model DDevelopment of 6 DOF nonlinear Aircraft Model DDevelopment of Steady State Trim Conditions DAlgorithmic Development of model in MATLAB D

Developmentof NonlinearF16 Aircraft

ModelDevelopment of Graphical Equivalent in the SIMULINK DResearch Review, theoretical development and ProblemFormulation

D

Design of the Fuzzy Logic Switching Scheme DDesign of a Multiple Reference Model for all ‘modes’ DDerivation of a Stable Adaptive Law D

Scheme 1

Development of Overall System and Application PD Developed, P Partially Developed, B Balance

Overall Dissertation Status (Contd.)

ProposedTasks Proposed Sub Tasks Status

Research Review, theoretical development and ProblemFormulation

D

Research Review on RBFNN design steps and issues DDesigning the Proposed RBFNN Architecture DDerivation of a Stable Adaptive Law and overall system DApplication of the developed scheme to a Nonlinear Process P

Scheme 2

Application of the developed Scheme to control F16Dynamics

B

Research Review, theoretical development and ProblemFormulation

D

Designing the Proposed RBFNN Architecture DDesign of the Fuzzy Logic Switching Scheme BDesign of a Multiple Reference Model suitable for all‘modes’

B

Development of Overall Scheme BApplication to a Nonlinear Process B

Scheme 3

Application for F16 Dynamics Control BD Developed, P Partially Developed, B Balance

a dissertation proposal presentation by sukumar kamalasadan

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