Exploring Engineering

Exploring Engineering

Chapter 10

Control Systems and Mechatronics

Topics to be Covered

Block Diagrams Transfer functions

Control systems Steady State Transient models

Mechatronics

Block diagramsMathematically mimic a small piece of a physical

process E.g., a stereo amplifier … see:

www.engr.uky.edu/.../index_files/image003.jpg

Block diagrams Notice the blocks show the connectivity and

gross function. They do not show the actual wires, printed circuits

etc that make a stereo receiver. The blocks can be broken down much further in

increasing detail of what is in a block

To be really useful, the blocks can be given a simple mathematical description that emulates just what they do

Transfer (Response) Function

Relates what signal goes in (e.g., volts. pressure, light source) to what goes out (e.g., amperes, mechanism movements, volts etc.) Simplest transfer function:

Transfer function:Output = Gain x input

Gain = 5

Simple gain transfer block

Input = 1(volts, amps,temperature,etc.

Output = 5(volts, amps,temperature,etc.

Transfer (Response) Function Cruise control – a string of blocks

representing the physical functions

Transfer (Response) Function If the transfer functions to first power

(a.k.a. “linear”) you can multiply them together

Open and closed loop controlFor your first cruise control, just put a

brick on the accelerator and sit back …

Brick controller

Engine system

Surroundings

DesiredSpeed, So

Fuel & air

ActualSpeed, S

Power

• If surroundings are head wind vs. tailwind, hills vs. flat,etc., will actual speed equal desired speed?

Open and closed loop controlOpen loop controls do not work wellClosed loop or feedback control is near

universal Feedback is made possible by a “comparator”

The desired controlled variable is called the “set point”

Desired Speed, So +

-

Actual Speed, S

Difference or error signalS0 -S

Feedback control

Comparator

Surroundings

Mathematics of Feedback Control

Collapse all the blocks; the gain Gp is the product of all the linear gains of the blocks The control is proportional is the output is a simple

multiple of the input.

ProportionalController; gain Gp

+-

SActS0

S0 - S

ActpAct SSGS 0

Mathematics of Control Blocks

ppAct

p

pAct

GG

SSS

G

SGS

1

100 error % the&

1-

iserror statesteady that theso 1

00

0

ActpAct SSGS 0

• Ops! Steady state error

• The moral is to watch your gains!

• So is an infinite gain the solution?

Gp % error

1 50

10 9.1

100 0.99

Transient Behavior If you have a steady state feedback loop

given by one or more transfer functions, that solution is a snapshot in time If you change the set point to another value, that

gives another snapshot of the state of the system What happens during the transient interval

between steady states? Can your model accommodate transients?

Transient Behavior Your model needs transient behavior built in

– which so far the proportional controller does not have

At a minimum for a cruise control you needa) The inertia of the car (it will not accelerate

instantaneously)

b) The wind resistance that varies as S3 and keeps the

car from speeding to speed

c) Perhaps an allowance for hills?

Transient BehaviorExcluding hills,a simple model would

include at least these blocks

Transient BehaviorWithout doing the arithmetic, results of

this model are as shown: a) low gain, b) medium gain and c) high gain

Transient Behavior Notice the sensitivity to the overall gain:

a) Too low and the transient is sluggish

b) Medium and it has some overshoot but settles down

c) Oscillatory behavior

Moral is watch your gains! High and low gains have their drawbacks!

Mechatronics Mechatronics is a

synthesis of mechanics, electronics, control engineering and computers

http://gizmodo.com/5342497/self+balancing-enicycle-is-like-a-segway-for-the-circus

Mechatronics Instead of first

doing a mechanical design, followed by an electronic design, followed by a control systems design they are all done coequally

Stepper motors are often mechatronic components

1

1

2

2

3

3

Windings and poles

Rotor

Figure 12: Principle of a stepper motor

1

1

2

2

3

3

Windings and poles

Rotor

1

1

2

2

3

3

Windings and poles

Rotor

Figure 12: Principle of a stepper motorPrinciple of a stepper motor

MechatronicsCan use a variant on a stepper motor

to replace two separate systems, a throttle and cruise control on a carhere’s how its done: http://video_demos.colostate.edu/mechatr

onics/index.html Go to: stepper motor PIC

-based position and speed controller

MechatronicsSuch technology will become common

place on cars as part of “fly-by-wire” methodology (used on most new passenger aircraft)

Summary Control depends on some simple abstractions:

Block diagrams that simulate an element in the control linkages (whether mechanical or otherwise)

Simple mathematical representation of the block’s function

A comparator to generate an error signal Feedback to correct the instantaneous value of the

controlled variable High proportional gain to reduce steady state error and

low gain to reduce unsteady transient behavior.

Mechatronics is an integrated method of design including mechanical, electronic and control elements.