Simulation, Block Diagrams and Feedback Control

8/3/2019 Simulation, Block Diagrams and Feedback Control

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ME 244L Prof. Raul G. LongoriaDynamic Systems and Controls Laboratory

Department of Mechanical EngineeringThe University of Texas at Austin

Simulation, Block Diagrams,

and Feedback Control

Prof. R.G. Longoria

Updated Fall 2009


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Overview

Using block diagrams to describe system model

equations

How block diagrams are used in practice

LabVIEW implementation quick demo Feedback control concepts

NOTE: Some of these slides were/are covered in

lecture, others are for information only.


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Example: Sphere in free fall

V

g

2

2

;

d b

d s

d

s

dpF p mV

dt

p F F mg

p mV K V gV mg

KV V g g

m

=

= += = +

= +

Newtons Law:

You can choosep (momentum) or V

(velocity) as your state variable. Here

we choose velocity.

2

3

1drag

2

1buoyancy

6

d D s

b s

F C AV

F gV g D

= =

= = =

Forces:


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Sphere in free fall block diagram

( )

2

2

1

d D s

s

V V

K m C A m

g

= += =

=

NOTE: The ANALOG diagram shown here is a model that is nowimplemented in many commercial block diagram simulation languages. This

is a computational diagram that embodies the mathematical model. This is

also a form used in feedback control diagram descriptions.

Simplify for formulation of

a block diagram:

x V=


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Block diagram algebraA pictorial representation of the functions performed

by each component and of the flow of signals.

Basic functions: gains, summers, integrators, etc.

Lines between blocks are signals, and blocks areoperators on the signals.

Can be used for linear or nonlinear dynamic systemsand controls descriptions.


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Block Diagram AlgebraSumming point

a b

a

b

+

Branching point

In general, systems operate on inputs to give

outputs.

( )y g u=Here,

yu

In linear systems, the signal variables are assumed

to be s-domain forms, while ifnonlinear it isassumed these are strictly time domain functions

(and Laplace transform does not apply).

For linear, ( ) ( ) ( )Y s G s U s=

( )g i

( )Y s( )U s( )G s


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ME 244L Prof. Raul G. LongoriaDynamic Systems and Controls Laboratory Department of Mechanical EngineeringThe University of Texas at Austin

Implemented first in analog

mg +

pp

KdF

Gain

Sum Integrate

From H.S. Baeck, Practical Servomechanism Design,

McGraw-Hill, 1968.


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Electronic analog simulation

A system can be wired into a patch panel, and

the simulation is instantaneous.

The set up is extremely difficult and error

prone; changing parameters can be limited. Output of data can be limited.

Electronics were not always reliable.


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Dark PastThe figure to the left (courtesy of a simulationgroup at Boeing that developed EASY5)

illustrates the complexity required in analog

integration, particularly for very complex systems.

The patch panels were difficult to manage, and

could have intermittent/unreliable connections.


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Modern (digital) implementations

Dont have the advantage of speed, but much

more versatile, reliable, etc.

Many implementations:

Boeing EASY5 (now owned by MSC) Matrixx (now owned by National Instruments)

Matlab/Simulink

National Instruments LabVIEW (Sim. Module)

(others)


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EASY5 allows you to integrate models built in different waysthey did this

early! (c. 1980s?)


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Matlab/Simulink

SourcesControllers

Basic linear Nonlinear Logical

Example: basic feedback diagram

The Matlab/Simulink environment

provides a way to implement block

diagram models directly for analysis

and simulation. These are just someof the basic elements available.

These types of operators are common in most

block diagram simulation environments (EASY5,

Simulink, LV Simulation. etc.)


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Quick LabVIEW Demo


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Building the sphere model


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How do you build a block diagram?

Derive the complete state equations (as you are

learning to do in ME 344)

Identify an integrator for each first order

equation have as many integrators as states

Use summers to form the algebra (add up the

RHS)

Form the terms that go into your summers byusing states being solved and inputs


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Example: Pushrod-lifter

State equations:

3 states1 input


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Block DiagramNOTE: Most block diagramsimulation programs include

a STATE-SPACE element

that can be used if you have

those equations.


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Feedback Control Systems

We introduce the basic concept of feedback

control, which takes advantage of measuredfeedback and error measurement to adjust

system action for a specified purpose.

E R Y = R

Y

+


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Identifying Feedback in Automatic

Feedback Control Systems*

The purpose of a feedback control system is to carry

out commands; the system maintains the controlledvariable equal to the command signal in spite of

external disturbances.

System operates as a closed loop with negativefeedback.

The system includes a sensing element and a

comparator, at least one of which can bedistinguished as a physically separate element.

*O. Mayr (1970)


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Float regulator (c. 280 B.C.)In his book, Mayr analyzes all types of

historical feedback control systems using

block diagrams.


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D. Macaulay (CD-ROM)

Does the governor in this toy control the mouse

speed in a feedback sense?


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Classification of control systems Open-loop the output has no effect on the control

action Closed-loop use of feedback to guide control action

Analog vs. Digital - refers to the difference in

implementing the controller, typically electronically Classical vs. Modern

Classical control usually refers to SISO (single-input/single-output) systems

MIMO (multiple-input/multiple-output) is concerned withcontrol of systems having more than one controlled variablewith possibly more than one control input

ME 364L

ME 384Q


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Open-Loop Control The output is not compared with the reference

(desired) signal/input

Susceptible to large errors due to:

Disturbances

Variation in the system parameters

Examples

Timed processes (e.g., toasters, most dryers, etc.)

In vehicle systems, many traction/braking systems

and steering systems are clearly open-loop


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Closed-Loop Control

Controller Plant

Sensor

Error

Signal

ReferenceSignal

+

++

Disturbance

Output

Feedback Signal

Plant any physical system to be controlledController can generate inputs to the plant to achieve a desired objective

Sensor means by which plant output is transformed to feedback information

We try to represent control systems using block diagram descriptions. This is

the standard form.


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Transfer functions Linear feedback controls make use of transfer functions. Note that SISO feedback does NOT have to be formed by linear

elements only. You can have nonlinear elements (later).

The transfer function of a linear, time-invariant, differentialequation system is defined as the ratio of the Laplace transformof the output to the Laplace transform of the input under theassumption that the initial conditions are zero.

zero initial conditions

1

1 1

11 1

[output]( )

[input]

( )

( )

m m

o m m

n no n n

G s

b s b s b s bY s

U s a s a s a s a

=

+ + + += =

+ + + +

L

L

A TF is aproperty of a system and independent of any input.


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Quick TF

Derivationfor MKD

Mass (M)

Spring (K)

Damper (D)

system


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Response of MKD to Force Input

2

1

ms bs k + +( )F t ( )x t

oF

onT

( )F t

t

Step function turns on at Ton

Implement in LV simulation


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Effect of Closing the Loop Advantages:

Provides for disturbance rejection

Reduces sensitivity to parameter variations

Use error signal for dynamic tracking

Enhance accuracy, extend bandwidth, etc.

Disadvantages:

Can lead to oscillation or instability


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Closed-Loop Control Model

r e u

-

+

( )cG s

errorcontroller

( )pG s+

( )H s

du

sy

mu

y

plant

measurement

1 1

p c p

d

c p c p

G G G y u r

G G H G G H = +

+ +

In ME 344 and ME 364L you learn how to analyze control systems, using block

diagram algebra to derive expressions for the closed-loop response in the form,


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Example:Closed-Loop Speed Control of a Gas Engine

( )R s e eT

-

+ 1

1 1

K

s +

Throttlecontroller

2 ( )G s

+

( )H s

dT

tT ( )C s

Engine Dynamics

measurement

1 2

1 21

C G G

R G G H = +

1( )G s

Speed

Ignore disturbance for now,

2

2 1

K

s +

1

1ms +

1

2

1sec

4sec

0.5secm

=

==

1

2

?

0.2

K

K

=

=

Note, sometimes the

values are easy tomeasure and form

basis of this

simplified model.


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ME 244L Prof. Raul G. Longoria

Dynamic Systems and Controls Laboratory Department of Mechanical EngineeringThe University of Texas at Austin

Basic Control Actions Proportional (P) control

Integral (I) control

Derivative (D) control

Combination: PI, PD, PID

( )cG s( )E s ( )U s

Most industrial controllers (well over 90 to 95%) you will

run across will be of a PID type.


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Proportional Control( )cG s

( )E s ( )U s

( ) ( )

p

p

u K e

U s K E s

=

=

( ) constantc pG s K= =

2

1X

F ms bs k =

+ +

Plant model

2

stiffness

1

1 1 1

p p pc

R p p p

K G K X GH

X GH K G ms bs k K

= = =

+ + + + +

Closed-loop

Control


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Other Basic Forms( ) ( )I II I

K Ku edt U s E s

T T s= =Integral control:

Integral control reduces or eliminates steady-state error, but has

reduced stability.

( ) ( ) D D D Dde

u K T U s K T sE sdt

= =Derivative control:

Derivative control yields an increase in effective damping,improving stability.

PID control:1

( ) 1 ( )DI

U s K T s E sT s

= + +

Most common in practical application.

Tuning required (Ziegler-Nichols)

Note on implementing

this with ODEs forsimulation.


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Summary Reviewed block diagram descriptions of system

models and control systems Described examples of how these methods are

used in industry/military applications

A quick demonstration of the LabVIEW

Simulation Module environment

Simulation, Block Diagrams and Feedback Control

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