EET273 Electronic Control Systems - PowerPoint Presentation

Slide1

EET273

Electronic Control Systems

Week

7

– Closed Loop ControlSlide2

Calibration Lab Recap

Calibrating a system element means correcting a system’s behavior so that it matches a desired transfer function

Notice that the

setpoint

you are giving the system was a percentage from 0-100%, so was the read-back from the tact board in the PLC software

Because the units match (both are percentages), we can directly compare these 2 quantities and calculate an error signal: (e = SP – PV)

With this error signal, we can now design some type of a controller, and finally use closed-loop feedback in our system!Slide3

Closed Loop Control

Readings: Ch. 29:1

–

29:5Slide4

Open Loop vs. Closed Loop

Open-loop:

Simple – no feedback mechanism, simply give the system an input, and get an output

Works for very simple systems, usually when the exact value of the PV is not critical, or the system load is very predictable.

Closed-loop:

Accurately track a process variable (PV)

Improve the overall performance of a system, typically this means reducing error quickly and with minimal overshoot/oscillations

Stabilize a process – an open loop system can “run away” and become unstable, but a properly designed closed loop system can prevent instability

But be careful, an improperly design control loop can actually turn a stable system into an unstable oneSlide5

Open-loop or closed-loop?

Hair dryer

Toaster

Light switch

Air conditioner

Dishwasher

Clothes dryer

In some systems, it depends on how we define the “system”

Ex: A car by itself is open-loop, but if the driver is part of the “system”, it’s actually closed-loop. Often humans are the “controller” in an otherwise open loop systemSlide6

Some definitions

Process – the physical system we wish to monitor and control

SP –

setpoint

– input to the control system

PV – process variable – output of the system

Controller –

module that processes the error term, and is applied to the plant input, with the purpose of reducing system error

Final Control Element (FCE) –

element that

is acting on the

process variable

Manipulated Variable (MV) or Output – Controller output variable

Open Loop – no feedback from output to input

Closed Loop – with feedback from output to inputSlide7

Closed Loop ControlSlide8

Design Criteria

Some control systems have very tight requirements for their outputs, and some are much more loose.

Which controller design you choose is typically based on the output requirements.

Systems with tight requirements:

Drone/quadcopter

Car cruise controller

Systems with more loose requirements:

Liquid buffer tank

Home heating system / thermostatSlide9

System Performance

What constitutes “good performance” in a system is

application

specific, and often subjective

3 ways to quantify “good performance” are:

Rise Time

5% - 95% - How quickly does the output go from 5% of the SP to 95% of the SP

Settling Time

Time it takes for output to settle within a certain percentage of the steady state value

Overshoot

More much more than the SP the output reaches on it’s initial overshootSlide10

System Performance

Rise time

How

quickly does the output go from

x%

of the SP to y

%

of the

SP

Typically

10% - 90%

or 5% - 95%Slide11

System Performance

Settling time

Time it takes for output to settle within a certain percentage of the steady state

value

Typically defined as 2% or 5% of steady state valueSlide12

System Performance

Overshoot

Magnitude of the initial PV overshoot above the SP

Usually defined as a percentage

Ex:

SP = 1V

PV peaks at 1.2V

1.2V – 1V = 0.2V

0.2V / 1V = 20% overshootSlide13

Controllers

A controller acts on the error signal (e), to modify the input to the plant

A controller design can be

S

imple – on/off control, proportional control

Complex – PID controlSlide14

Controllers

We can simplify this system, using the same formula: TF = G / (1 + GH)

Except now, G is actually K*G

So, the simplification of this system is: TF = KG / (1+ KGH)Slide15

On/Off Control

Controller output is binary – either 100% ON or 100% OFF

Very simple control algorithm, switches input on or off based on relationship between process variable (PV) and

setpoint

(SP)

If PV > USP then

Controller = “OFF”

If PV < LSP then

Controller = “ON”

Some applications this may be fine

Ex. Water level in a buffer tank

Ex. Heating system in your home

Others may require more precise control

Ex. Car cruise control systemSlide16

Proportional Control

Rather than simply comparing the error to a value and making a binary (ON/OFF) decision, we can design a controller to respond to the

magnitude

of the error

Large error

 Large error correction

Small error

 Small error correction

A proportional controller simply takes the error, and multiplies it by some scaling factor (gain), commonly known as

Tuning a proportional controller simply means adjusting or tuning

 Slide17

Proportional Control

Proportional controllers react to the magnitude of the error

This error is the difference between the PV and the SPSlide18

Proportional Control

Direct-acting controller – output in same direction as PV

Reverse-acting controller – output in opposite direction as PVSlide19

Proportional Control

Another way to refer to gain is the term “Proportional Band”

Ex:

For

= 5



PB = 1/5 = 0.2 = 20%

The intuition behind this is: If a gain of 5 is required, that means the input to the controller is only 20% of what we’d like it to be (20% * 5 = 100%)

 Slide20

Proportional Control

How to set the proportional gain,

?

Setting

is equivalent to ON/OFF control

This is how an op-amp comparator works – open-loop gain of an op-amp is infinite

How much gain a proportional controller needs depends on the process, and the elements in the control loop

Often, finding a good value for

is a process of trial and error, and a balancing act of system requirements

 Slide21

Proportional Control

Too much gain can result in overshoot as the controller converges on the SP

Too little gain can results in a PV that cannot respond quickly enough to SP/process changes.Slide22

Proportional-only offset

Proportional-only

offset occurs when:

Proportional control is the only type of control (hence the name)

A load is present in the system

In the world of control, a load is:

Anything that tends to induce error into the system:

Motor: Friction/physical load

Car: air resistance/friction

Buffer tank: water leaving the outletSlide23

Proportional-only offset

In a proportionally controlled system, any load on a system results in a PV that never fully reaches SP

Remember, as the error is reduced, the amount of error correction is reduced (this is how proportional control works)

If the load on a system = amount of error correction, the system will reach an equilibrium below the SP.

Less gain:

M

ore offset

S

lower response (less chance of oscillation)

More gain:

Less offset

Faster response (may oscillate)Slide24

Proportional-only offset

Ex:

A buffer tank has a proportional controller controlling an inlet valve, an outlet

The inlet valve flow rate has a range of 0-100 GPM

If there no load on the system (no water is exiting the system), the PV (water level) will eventually reach the SP

But what if there is an outlet with a flow rate of 10 GPM?

As the tank fills, the error reduces, and the valve closes proportionally

When the inlet rate = outlet rate (10 GPM), an equilibrium is achieved, and the tank level remains constant

This produces a steady state error, and the water level never reaches the SPSlide25

Proportional-only offset

This

effect can be reduced by increasing the gain

, but this can cause oscillations

A well tuned proportional controller is often a compromise between excessive oscillations and excessive offset.

 Slide26

Proportional-only offset

Can we fix this offset with a bias adjustment?

We can try, but it won’t work well

Any change in load will create a new offset value, and we would need to re-bias the new offset

To truly solve this problem, we need…integral control (

next lecture)Slide27

Proportional Control Example

PID control of a DC motor’s position:

https://

www.youtube.com/watch?v=fusr9eTceEo

Ball and Plate:

https://

www.youtube.com/watch?v=j4OmVLc_oDw

Control system simulator:

http://

www.facstaff.bucknell.edu/mastascu/eControlHTML/Intro/IntroWithProblems/Intro00.htmlSlide28

Lab

Closed loop intro

Controlling the motor speed via on/off and PID control methods

“Loading” the motor with the blue potentiometerSlide29

Midterm – Week 6

No Quiz on this weeks material (closed loop control)

Transfer Functions

How to combine transfer functions in series

How to simplify a closed loop system into a single block

Ladder Logic

Identify different ladder logic symbols

Draw a ladder logic diagram from a schematic and vice versa

Identify the operation of basic ladder logic circuits

Sensors/Switches

Identify different types of sensors

Identify normal state, NO, NC, and understand what type of even triggers a switch/sensor

4-20mA Signaling/Calibration

Terms/definitions – live zero, span, zero, etc.

Identifying types of calibration errors, span error, zero error, linearity error, hysteresis error