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A Java Based Interactive Control Design and Tuning Platform

A Java Based Interactive Control Design and Tuning Platform

Aaron Radke 7/9/3

7/9/3

Aaron Radke

Page 1

A Java Based Interactive Control Design and Tuning Platform

Outline

• Introduction
• Software Structure

– Structural Implementation – Data Flow Implementation

• System Functionalities and Application

– Differential Equation Solvers – Controller Design and Implementation – General Model

• Summary and Future

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Introduction

Introduction

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Introduction ⇒ Existing software tools

Existing software tools

• Matlab

⋄ Matlab is powerful Figure 1: Matlab ⋄ It is a controls standard ⋄ Simulink allows easy set up nonlinear systems

• Shortcomings of Matlab

⋄ Simulink is great but tuning is tedious

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Introduction ⇒ Existing software tools ⋄ Matlab has GUI but it takes a bit of programming to use ⋄ Matlab license issues ⋄ Version problems

• SysQuake

Figure 2: SysQuake ⋄ Free package with syntax similar to Matlab ⋄ Built around real time dragging

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Introduction ⇒ Existing software tools Figure 3: SysQuake icon ⋄ Led to the first project with simplicity of NPID tuning

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Introduction ⇒ Existing software tools Figure 4: SysQuake window

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Introduction ⇒ Existing software tools

• Shortcomings of SysQuake

⋄ Changing the system needed differential equation derivations

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Introduction ⇒ Proposed approach

Proposed approach

• Problem formulation

⋄ Start new with difference equations ⋄ Real-time functionality

• Software development strategy

⋄ Development language Figure 5: Java logo ⋄ Free ⋄ Accessible

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Introduction ⇒ Proposed approach ⋄ Powerful framework ⋄ Structure

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Introduction ⇒ Software requirements and specifications

Software requirements and specifications

• A real time, interactive, dynamic tuning environment

for control systems.

• Extensible framework
• Simple construction of nonlinear systems
• Cross-platform, web application deployment
• Capability of presenting new control designs and

algorithms

• Useful and practical for implementation

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Structural Implementation

Structural Implementation

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Structural Implementation ⇒ Focus on difference equations

Focus on difference equations

• Start with the core difference equation solver method
• The GUI can be built later

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Structural Implementation ⇒ Fundamental building blocks

Fundamental building blocks

• Object orientedness

⋄ Library of blocks

• SimBlocks

⋄ SimSource ⋄ SimFunction ⋄ SimSink ⋄ Class inheritance structure diagrams

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Structural Implementation ⇒ Fundamental building blocks

JLabel ScrollablePicture SimZtf Sim1stOrder Sim2ndOrder SimStf SimDoubleIntegrator SimIntegrator SimFunction SimAdd SimFunctionFactory SimDiffEq SimDTOC SimFunctionSelector SimGain SimGFunc SimSaturation SimStat SimSubtract SimZtfDirect SimADRC SimDTOCDiff SimFunctionTest SimGeneralClasicController SimNPID SimTest SimBase SimBlock SimParameters SimVariable VariableContainer SimBuffer SimSource SimFactory SimInput SimFunction2Input SimFunctionXInput SimImage SimSourceFactory SimContinuousProfile SimProfile SimTrapezoidalProfile SimDialogManager SimDiff SimFilter SimPid SimDisturbance SimDoubleTriangle SimNoise SimNothing SimPolyProfile SimSourceSelector SimStep SimTimeIndex SimTrapezoid SimSink SimMultiply JApplet SimImageFactory ADRC GCADRC GeneralControlLoop SimpleLoop SimpleLoopNN TestBlock SimNPIDwc SimPtPlot SimStdout SimTextBoxOutput SimCheckBox SimComboBox SimDoubleArray SimNumber SimString SimTextBox SimComboBoxNumber SimComboBoxString SimInteger SimStaticNumber implements Console

Figure 6: The class structure for the blocks (without implementation classes)

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Structural Implementation ⇒ Fundamental building blocks

Figure 7: The entire hierarchal class structure of the project

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Structural Implementation ⇒ Fundamental building blocks

• Class inheritance structure

SimPid → SimStf → SimZtf → SimDiffEq → SimFunction → SimBlock → SimBase (1) Table 1: Example hierarchy path of a PID controller Class name provides SimBase simple title and description structures SimBlock the ability to interface with the rest of the simulation library

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Structural Implementation ⇒ Fundamental building blocks SimFunction the functionality of inputs and

• utputs

SimDiffEq the ability to create, display, and edit discrete difference equations SimZtf the ability to create, display, and edit z transfer functions and convert them to discrete difference equations SimStf the ability to create, display, and edit s transfer functions and convert them to z transfer functions

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Structural Implementation ⇒ Fundamental building blocks SimPid the specific transfer function for proportional, integral and derivative control

• Block interconnection
• Small memory size
• Block interconnection method

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Structural Implementation ⇒ GUI development

GUI development

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Structural Implementation ⇒ GUI development Figure 8: Screen shot for the sample simtk applet GUI

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Data Flow Implementation

Data Flow Implementation

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Data Flow Implementation ⇒ Developer’s viewpoint

Developer’s viewpoint

• Top-level managing class

⋄ Hierarchy ⋄ SimFactory ⋄ Containment structure of example applets

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Data Flow Implementation ⇒ Developer’s viewpoint

GeneralControlLoop SimParameters SimFactory SimTextBoxOutput SimPtPlot SimImage SimSubtract SimFunctionSelector SimStep SimSourceSelector SimGain SimADRC SimAdd SimGeneralClasicController SimProfile SimSource SimFunction SimSink SimBlock Simulatable SimBuffer SimPanelable Simulation SimTabBox SimDiffEq SimFucntionSelector SimComboBoxString SimNumber Simple SimFunctionFactory

Figure 9: Simplified example containment of classes for the Gener- alControlLoop applet

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Data Flow Implementation ⇒ Developer’s viewpoint

• Setting up a simulation

⋄ Loading or instantiating blocks ⋄ Adding and connecting blocks ⋄ Simulating

• Building blocks

⋄ Extend a block ⋄ Add adjustable variables ⋄ Override iteration definition

• Developer’s documentation

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Data Flow Implementation ⇒ User’s viewpoint

User’s viewpoint

• Nature of the system
• Simulation accuracy
• Globals

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Comparison of Ode Solvers

Comparison of Ode Solvers

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Comparison of Ode Solvers ⇒ Simple example problem for comparisons

Simple example problem for comparisons

• Applet Source

y′(t) = f(t, y(t)) (2) y(t0) = y0 (3)

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Comparison of Ode Solvers ⇒ Simple example problem for comparisons Figure 10: Comparison of ode solvers with 5 iterations

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Comparison of Ode Solvers ⇒ Simple example problem for comparisons Figure 11: Comparison of ode solvers with 20 iterations

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Comparison of Ode Solvers ⇒ Simple example problem for comparisons Figure 12: Comparison of ode solvers with 200 iterations

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Comparison of Ode Solvers ⇒ Conclusion

Conclusion

• Ten-fold increase of Tustin over Simple Euler

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Differential Equation Solver Engine

Differential Equation Solver Engine

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Differential Equation Solver Engine ⇒ Specific conversions from continuous form to discrete

Specific conversions from continuous form to discrete

• Simple Euler

s = −1 + z z (4) ⋄ Integrator 1 s → z −1 + z (5) ⋄ Double Integrator 1 s2 → z2 1 − 2 z + z2 (6) ⋄ The problem with the Simple Euler method

• Tustin

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Differential Equation Solver Engine ⇒ Specific conversions from continuous form to discrete s = 2 (−1 + z) T (1 + z) (7) ⋄ Integrator 1 s → T + T z −2 + 2 z (8) ⋄ Double Integrator 1 s2 → T 2 + 2 T 2 z + T 2 z2 4 − 8 z + 4 z2 (9) ⋄ First order plant 1 s + a → T + T z −2 + a T + 2 z + a T z (10) ⋄ Second order plant

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Differential Equation Solver Engine ⇒ Specific conversions from continuous form to discrete ω2 s2 + 2ζω + ω2 → T 2 ω2 + 2 T 2 z ω2 + T 2 z2 ω2 4 − 4 T ζ ω + T 2 ω2 + 2 z (−4 + T 2 ω2) + z2 (4 + 4 T ζ ω + T 2 ω2) (11) ⋄ Second order plant with ω = ζ = 1 1 s2 + 2 + ω2 → T 2 + 2 T 2 z + T 2 z2 4 − 4 T + T 2 − 8 z + 2 T 2 z + 4 z2 + 4 T z2 + T 2 z2 (12) ⋄ PID controller continuous to discrete kps + kds2 + ki s → 4 kd − 2 kp T + ki T 2 − 8 kd z + 2 ki T 2 z + 4 kd z2 + 2 kp T z2 + ki T 2 z2 −2 T + 2 T z2 (13)

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Differential Equation Solver Engine ⇒ Specific conversions from continuous form to discrete ⋄ Approximate differentiator s (τs + 1)2 → −2 T + 2 T z2 T 2 + 2 T 2 z + T 2 z2 − 4 T τ + 4 T z2 τ + 4 τ 2 − 8 z τ 2 + 4 z2 τ 2 (14)

• General transfer function derivations

Gp = n0 (15) n0. (16) Gp = n1s + n0 (17)

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Differential Equation Solver Engine ⇒ Specific conversions from continuous form to discrete −2 n1 + n0 T + 2 n1 z + n0 T z. (18) Gp = n2s2 + n1s + n0 (19) 4 n2 − 2 n1 T + n0 T 2 − 8 n2 z +2 n0 T 2 z + 4 n2 z2 + 2 n1 T z2 + n0 T 2 z2. (20) Gp = n3s3 + n2s2 + n1s + n0 (21)

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Differential Equation Solver Engine ⇒ Specific conversions from continuous form to discrete −8 n3 + 4 n2 T − 2 n1 T 2 + n0 T 3 +24 n3 z − 4 n2 T z − 2 n1 T 2 z + 3 n0 T 3 z −24 n3 z2 − 4 n2 T z2 + 2 n1 T 2 z2 + 3 n0 T 3 z2 + 8 n3 z3 +4 n2 T z3 + 2 n1 T 2 z3 + n0 T 3 z3. (22) Gp = n4s4 + n3s3 + n2s2 + n1s + n0 (23) 16 n4 − 8 n3 T + 4 n2 T 2 − 2 n1 T 3 + n0 T 4 − 64 n4 z + 16 n3 T z −4 n1 T 3 z + 4 n0 T 4 z + 96 n4 z2 − 8 n2 T 2 z2 + 6 n0 T 4 z2 − 64 n4 z3 −16 n3 T z3 + 4 n1 T 3 z3 + 4 n0 T 4 z3 + 16 n4 z4 +8 n3 T z4 + 4 n2 T 2 z4 + 2 n1 T 3 z4 + n0 T 4 z4. (24)

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Differential Equation Solver Engine ⇒ General s to z transform matrices

General s to z transform matrices

Zn = Mn · Sn · Tn (25) Sn =           s0 s1 s2 . . . sn           (26)

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Differential Equation Solver Engine ⇒ General s to z transform matrices Tn =           T 0 T 1 T 2 . . . T n           (27)

• Conversion matrixes

M0 =

• 1
• (28)

M1 =   −2 1 2 1   (29)

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Differential Equation Solver Engine ⇒ General s to z transform matrices M2 =     −4 −2 1 −8 2 4 2 1     (30) M3 =        −8 4 −2 1 24 −4 −2 3 −24 −4 2 3 8 4 2 1        (31) M4 =           −16 −8 4 −2 1 −64 16 −4 4 −96 −8 6 −64 −16 4 4 16 8 4 2 1           (32)

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Differential Equation Solver Engine ⇒ General s to z transform matrices Listing 1: S transform to z transform algorithm

for ( int i = 0 ; i<=order ; i ++){ // loop through zˆ i terms // loop each c o e f f i c i e n t ( which i s also Tˆ j terms ) for ( int j = 0 ; j<=order ; j ++){ // c o n t i n u a l l y add up terms for the coef

• f

zˆ i // s t o r i n g them into zpoly in the form

• f

zˆ3+zˆ2+z ˆ1 // from MSZ to LSZ zpoly [ order − i ] += c2dmatrix [ i ] [ j ] ∗ Tz [ j ] ; } }

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Differential Equation Solver Engine ⇒ General z transfer function to difference equations

General z transfer function to difference equations

y r = n0z4 + n1z3 + n2z2 + n3z1 + n4z0 d0z4 + d1z3 + d2z2 + d3z1 + d4z0 (33) z−4 z−4 (34) y = 1 d0 ((n0r + n1rz−1 + n2rz−2 + n3z−3 + n4z−4) −(d1rz−1 + d2rz−2 + d3z−3 + d4z−4)) (35) y = q

i=1(nirz−i − dirz−i) + n0r

d0 (36) z−i → y(k − i) (37)

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Differential Equation Solver Engine ⇒ General z transfer function to difference equations Listing 2: z transform to difference equation algorithm

double tempsumterms = 0; for ( int i =1; i<=zorder ; i ++){ tempsumterms += num[ i ] ∗ in . val [ i ] − den [ i ] ∗ out . val [ i ] ; } ;

• ut . val [ 0 ] = (

tempsumterms + num[ 0 ] ∗ in . val [ 0 ] ) / den [ 0 ] ;

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Controller Design and Implementation

Controller Design and Implementation

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Controller Design and Implementation ⇒ Parameterization

Parameterization

kd = 2ωc (38) kp = ω2

c

(39)

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Controller Design and Implementation ⇒ Approximate PID

Approximate PID

u = kpe + ki

• e + kd ˙

e (40) ˙ u = kp ˙ e + kie + kd¨ e (41) u(s) e(s) = kp + ki s + kd´ s (42) ´ s = s (τs + 1)2 (43)

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Controller Design and Implementation ⇒ Approximate PID

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1 2 3 4 5 6 7 8 9 10 time m a g n i t u d e

step tau = 1 tau = 0.25 tau = 5

Figure 13: 2nd order approximate derivative with tau=1,0.5,0.25 on a step function u(s) e(s) = kp + ki s + kd s (τs + 1)2 (44)

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Controller Design and Implementation ⇒ Approximate PID u(s) e(s) = s3(kpτ 2) + s2(kd + 2kpτ + kiτ 2) + s(kp + 2kiτ) + ki s3(τ 2) + s2(2τ) + s(1) + s(0) (45)

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Controller Design and Implementation ⇒ Nonlinear PID

Nonlinear PID

• Extension of classical PID

u = Gkp(e)e + Gki(e)

• e + Gkd(e)˙

e (46)

• Gfunc

10 20 30 40 50 1 2 3 4 5 6 7 8 9 10 time m a g n i t u d e

Figure 14: Nonlinear GFunction

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Controller Design and Implementation ⇒ Nonlinear PID Gx(e, kp1, kp2, kn1, kn2, wp, wn) =                e > 0    e · kp1 |e| < wp e · kp2 |e| ≥ wp e ≤ 0    e · kn1 |e| < np e · kn2 |e| ≥ np (47)

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Controller Design and Implementation ⇒ Active Disturbance Rejection Control

Active Disturbance Rejection Control

˙ x1 = x2 (48) ˙ x2 = x3 + b0u ˙ x3 = h(t) ˙ z1 = z2 + B1(y − z1) (49) ˙ z2 = z3 + B2(y − z1) + b0u ˙ z3 = B3(y − z1) u = u0 − z3 b0 (50)

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Controller Design and Implementation ⇒ Active Disturbance Rejection Control

r r y+n u ADRC general controller pre-filter (includes controller and observer) feedback-filter (includes controller and observer)

Figure 15: ADRC block diagram controller depicting the separation into two transfer functions U(s) R(s) = ω2

c

• 1

3ωo 3ω2

• ω3
• · S

b0 [(1) (3ωo + 2ωc) (3ωo2ωc + ω2

c + 3ω2

• )

(0)] · S (51)

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Controller Design and Implementation ⇒ Active Disturbance Rejection Control Y (s) R(s) = ω2

c

• (3ωoω2

c + 3ω2

• 2ωc + ω3
• )

(3ω2

• ω2

c + ω3

• 2ωc)

(ω3

• ω3

c)

• · S

b0 [(1) (3ωo + 2ωc) (3ωo2ωc + ω2

c + 3ω2

• )

(0)] · S (52) S =        s3 s2 s1 s        (53) b0 = Largest plant numerator coefficient Highest order plant denominator coefficient (54)

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Controller Design and Implementation ⇒ Discrete Time Optimal Control

Discrete Time Optimal Control

u = −rsign

• x1 + x2|x2|

2r

• (55)

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Controller Design and Implementation ⇒ Discrete Time Optimal Control u = fst(x1, x2, r, h) (56) d = rh d0 = hd y = x1 + hx2 a0 =

• d2 + 8r|y|

a =    x2 + a0−d

2

sign(y), |y| > d0 x2 + y

h,

|y| ≤ d0 fst = −    rsign(a), |a| > d r a

d,

|a| ≤ d

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A General Model Diagram

A General Model Diagram

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A General Model Diagram ⇒ Classic system

Classic system

controller plant

• utput

input

Figure 16: Simple classic controller without noise or disturbance

controller plant

• utput

sensor noise input disturbance r e y+n u y

Figure 17: Classic controller model setup with noise and disturbance

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A General Model Diagram ⇒ Combined General System

Combined General System

plant r y+n u y controller

• utput

sensor noise input disturbance

Figure 18: New General controller model setup

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A General Model Diagram ⇒ General Blocks

General Blocks

r y+n u general controller 2 inputs one output

Figure 19: New General controller block

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A General Model Diagram ⇒ General Blocks

r y+n u improved general controller pre-filter feedback-filter e classic controller ( ex. PID )

Figure 20: Improved General controller to include pre-filter and ob- server before summing loop

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A General Model Diagram ⇒ General Blocks

r e y+n u general controller example classic controller ( ex. PID )

Figure 21: New General controller block example using PID

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A General Model Diagram ⇒ General Blocks

r r y+n u ADRC general controller pre-filter (includes controller and observer) feedback-filter (includes controller and observer)

Figure 22: ADRC Controller (which is a special case of the improved general controller where error controller is unity)

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Summary and Future Research

Summary and Future Research

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Summary and Future Research ⇒ Summary

Summary

⋄ A real time, interactive, dynamic tuning environment for control systems. ⋄ Extensible framework ⋄ Simple construction of nonlinear systems ⋄ Cross-platform, web application deployment, ⋄ Useful and practical for implementation

• Simulation building blocks
• Simple GUI examples

⋄ Teaching tool ⋄ Capability of presenting new control designs and algorithms

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Summary and Future Research ⇒ Future research

Future research

• Additional library blocks
• Graphical setup of SimBlocks
• Extension to a hardware tuning and monitoring

interface ⋄ Use the library to find new tuning parameters ⋄ Network protocols

• Extension to Automated Computer Assisted Design

for Controls

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Project Tools

Project Tools

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Project Tools ⇒ Software Packages

Software Packages

• Java
• Mathematica
• SysQuake
• Matlab
• Ptolemy
• Java math exploration
• Octave
• Perl
• Gnuplot
• Simple ode solvers
• Hartmath

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Project Tools ⇒ Software Packages

• Vim
• Graphviz
• L

A

T EX

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Project Tools ⇒ Constructed tools

Constructed tools

• Aaindex
• Aao2tex
• Aao2pdf
• Aao.vim
• Java2dot
• Containment
• Aao2dot
• ExtractClassInfo
• Compressgif
• Csuthesis.sty

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Http://academic.csuohio.edu/aerl/simtk

Http://academic.csuohio.edu/aerl/simtk

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Demo

Demo

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Demo

List of Slides

2 Outline 3 Introduction 4 Existing software tools 9 Proposed approach 11 Software requirements and specifications 12 Structural Implementation 13 Focus on difference equations 14 Fundamental building blocks 20 GUI development 22 Data Flow Implementation 23 Developer’s viewpoint

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Demo 26 User’s viewpoint 27 Comparison of Ode Solvers 28 Simple example problem for comparisons 32 Conclusion 33 Differential Equation Solver Engine 34 Specific conversions from continuous form to discrete 40 General s to z transform matrices 44 General z transfer function to difference equations 46 Controller Design and Implementation 47 Parameterization 48 Approximate PID 51 Nonlinear PID 53 Active Disturbance Rejection Control

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Demo 56 Discrete Time Optimal Control 58 A General Model Diagram 59 Classic system 60 Combined General System 61 General Blocks 65 Summary and Future Research 66 Summary 67 Future research 68 Project Tools 69 Software Packages 71 Constructed tools 72 Http://academic.csuohio.edu/aerl/simtk 73 Demo

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Index

L

AT

EX, 70 A General Model Diagram, 58 A real time, interactive, dynamic tuning environment for control systems., 11 aaindex, 71, 76-1 Aaindex, 71 aao.vim, 71, 76-1 Aao.vim, 71 aao2dot, 71, 76-1 Aao2dot, 71 aao2pdf, 71, 76-1 Aao2pdf, 71 aao2tex, 71, 76-1 Aao2tex, 71 Active Disturbance Rejection Con- trol, 53 Additional library blocks, 67 Applet Source, 28 Approximate PID, 48 Block interconnection, 19 Block interconnection method, 19 Building blocks, 25 Capability of presenting new con- trol designs and algo- rithms, 11 Class inheritance structure, 17 Classic system, 59 Combined General System, 60 Comparison of Ode Solvers, 27 76-1

Demo compressgif, 71, 76-2 Compressgif, 71 Conclusion, 32 Constructed tools, 71 containment, 71, 76-2 Containment, 71 Controller Design and Implemen- tation, 46 Conversion matrixes, 41 Cross-platform, web application deployment, 11 csuthesis.sty, 71, 76-2 Csuthesis.sty, 71 Data Flow Implementation, 22 Demo, 73 Developer’s documentation, 25 Developer’s viewpoint, 23 Differential Equation Solver En- gine, 33 Discrete Time Optimal Control, 56 Existing software tools, 4 Extensible framework, 11 Extension of classical PID, 51 Extension to a hardware tuning and monitoring interface, 67 Extension to Automated Com- puter Assisted Design for Controls, 67 extractClassInfo, 71, 76-2 ExtractClassInfo, 71 Focus on difference equations, 13 Fundamental building blocks, 14 Future research, 67

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Demo General s to z transform matri- ces, 40 General z transfer function to dif- ference equations, 44 General Blocks, 61 General transfer function deriva- tions, 37 Gfunc, 51 Globals, 26 Gnuplot, 69 Graphical setup of SimBlocks, 67 Graphviz, 70 GUI development, 20 Hartmath, 69 Http://academic.csuohio.edu/aerl/simtk, 72 Introduction, 3 Java, 69 Java math exploration, 69 java2dot, 71, 76-3 Java2dot, 71 Mathematica, 69 Matlab, 4, 69 Nature of the system, 26 Nonlinear PID, 51 Object orientedness, 14 Octave, 69 Parameterization, 47 Perl, 69 Problem formulation, 9 Project Tools, 68 Proposed approach, 9 Ptolemy, 69

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Demo Setting up a simulation, 25 Shortcomings of Matlab, 4 Shortcomings of SysQuake, 8 SimBlocks, 14 Simple construction of nonlinear systems, 11 Simple Euler, 34 Simple example problem for com- parisons, 28 Simple GUI examples, 66 Simple ode solvers, 69 Simulation accuracy, 26 Simulation building blocks, 66 Small memory size, 19 Software development strategy, 9 Software Packages, 69 Software requirements and spec- ifications, 11 Specific conversions from contin- uous form to discrete, 34 Start with the core difference equa- tion solver method, 13 Structural Implementation, 12 Summary, 66 Summary and Future Research, 65 SysQuake, 5, 69 Ten-fold increase of Tustin over Simple Euler, 32 The GUI can be built later, 13 Top-level managing class, 23 Tustin, 34 Useful and practical for imple- mentation, 11

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Demo User’s viewpoint, 26 Vim, 69

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