Control?

Plot 1. Input distance to car suspension system from car

going up curb (a step) over time.2. Output distance of driver in the same time.

Time

Why Use Control?

Achieve the aims of your system efficiently and effectively– track reference

– speed of response

– avoid overshoots

– avoid steady-state errors

Autonomous operation

Avoid disturbances

Understand natural systems

What is a System?

Environment

System System System

InputsOutputs

Boundary

Systems are built of signals (variables), constants and differential operators

Systems are built of sub-systems!

Are Systems Perfect?

1. Open eyes:Extend your arms out at shoulder heightTouch the tips of your little fingers in front of

your nose!

2. Close eyes:Extend your arms out at shoulder heightTouch the tips of your little fingers in front of

your nose!

3. Strangeness:Make a circle with your right foot going in the

clockwise position.  While you are doing that, draw a six with your

right hand.

Open v Closed loop

Tutorial questions:

1. Explain the advantages and disadvantages of open loop control.

2. Explain the advantages and disadvantages of closed loop control

(closed loop control is sometimes called feedback control)

Open v Closed loop

1. Open loop is simple to implement but does not know the actual value of the control variable so is vulnerable to changing the conditions.

2. Closed loop accounts for changes in conditions, but at the expense of increased complexity and can become unstable if care is not taken in its design.

Feedback

The output signal is fed back to the input signal.

Inputs System Outputs

As an introduction, consider dynamic systems:

these change with time

As an example consider water system with two tanks

Water will flow from first tank to second

When will it stop following?

Dynamic Systems

IF

L

Stops when levels equal.

Why stop then? Why flow at all?

Plot time response of system….?

Level change – not instantaneous

• Initially:

Large height difference Large flow L up a lot

• Then:

Height difference less Less flow L increases, but by less

• Later:

Height difference ‘lesser’ Less flow L up, but by less, etc

Graphically we can thus argue the variation of level L and flow F is:

Dynamic Flow

F

tTT

L

t

I

We have dynamic equation for L in terms of I:

Put into ‘s’ domain to get output over input function:

Add a unit step input for I:

Integrate to determine variation of L

As t gets larger, exponential term disappears, L tends to Input.

Time Response

FI/R

tT

0.37I/R0.63I

T

L

t

I

We have dynamic equation:

Put into ‘s’ domain and rearrange:

Add a unit step input for I:

Integrate to determine variation of L

As t gets larger, exponential term disappears, L tends to Input.

Time Response

T

t-

e-1L

FI/R

tT

0.37I/R0.63I

T

L

t

I

R*C

LI

dt

dL

R*C

LIsL

IL R*C*sL s R*C1

1

I

L

Rs*C1

11L

s

Laplace operator ‘s’

Reminder from ENGR201

Know how components behave in an instant of time

Consider differential response

Combine and simplify into standard forms

Integration by lookup table determines long-term response

t domain s domain

Systems

An engineering system is a set of components connected together to accomplish a useful task

When building up a model system:

• Components should be easily identifiable

• Components should have a simple and clearly defined interaction with other components

• Components numbers should be minimised

Systems

In order to analyse a system:We identify an input signal

[a variable]Using block diagram components

[Basic block Summing junction Take-off point]

We combine internal signals[modified variables]

To produce the output signal[another variable].

The Input-Output relationship may then be determined

Car suspension model:

• Mechanical system

Explain what happens when a car goes over a bump?

www.superbike-coach.com

Car suspension model:

Explain what happens when a car goes over a bump?

x

finput

Simplify to single-input-single-output system

Form individual component models

Determine their relationships (use physical laws!)

Combine (and simplify if possible)

This gives us an instantaneous differential equation, but want a time response!

Spring

Damper

Mass

Source Nise 2004

tf

tx

tf

tx

tf

tx

Car suspension model:

Tutorial question

Determine the block diagram for each component?

Source Nise 2004

Textbooks

Martin Hargreaves, Engineering Systems - Modelling & Control, Longman

Kevin Warwick, An Introduction To Control Systems, World Scientific

N. Nise, Control Systems Engineering 6th Ed., J Wiley & Sons

ISBN 0471366013

+ Ogato + Zak + Dorf and Bishop...

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