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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
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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
Adjustment Mechanism
-
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
Adjustment Mechanism
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
Adjustment Mechanism
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
Adjustment Mechanism
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
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)
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)
I
II
III
Proposed Scheme I( Linear parametric “Jump” System)
Proposed Scheme I( Linear parametric “Jump” System)
Proposed Scheme I( Pitch Rate Control of F-16 Aircraft)
Proposed Scheme I( Pitch Rate Control of F-16 Aircraft)
Proposed Scheme I( Pitch Rate Control of F-16 Aircraft)
Proposed Scheme I( Pitch Rate Control of F-16 Aircraft)
Proposed Scheme II(Nonlinear Functional Uncertain System)
Single Link Robotic Manipulator with Payload
Neural Network Inversion
Desired Position
Desired Other States
Actual Position
Proposed Scheme II(Nonlinear Functional Uncertain System)
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
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