1. Electronic Control Systems Week 7 – Closed Loop Control
EET273
Electronic Control Systems
Week 7 – Closed Loop Control

2. 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!

3. Closed Loop Control
Readings: Ch. 29:1 – 29:5

4. Open Loop vs. Closed 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 one

5. 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 system

6. 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 input

7. Closed Loop Control

8. 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 / thermostat

9. 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 overshoot

10. 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%

11. 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 value

12. 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% overshoot

13. Controllers
A controller acts on the error signal (e), to modify the input to the plant
A controller design can be
Simple – on/off control, proportional control
Complex – PID control

14. 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)

15. 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 system

16. 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 𝐾 𝑃
Tuning a proportional controller simply means adjusting or tuning 𝐾 𝑃

17. Proportional Control
Proportional controllers react to the magnitude of the error
This error is the difference between the PV and the SP

18. Proportional Control
Direct-acting controller – output in same direction as PV
Reverse-acting controller – output in opposite direction as PV

19. Proportional Control
Another way to refer to gain is the term “Proportional Band”
Ex:
For 𝐾 𝑃 = 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%)

20. Proportional Control How to set the proportional gain, 𝐾 𝑃 ?
Setting 𝐾 𝑃 =∞ 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 𝐾 𝑃 is a process of trial and error, and a balancing act of system requirements

21. 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.

22. 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 outlet

23. 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:
More offset
Slower response (less chance of oscillation)
More gain:
Less offset
Faster response (may oscillate)

24. 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 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 SP

25. Proportional-only offset
This effect can be reduced by increasing the gain 𝐾 𝑃 , but this can cause oscillations
A well tuned proportional controller is often a compromise between excessive oscillations and excessive offset.

26. 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)

27. Proportional Control Example
PID control of a DC motor’s position:
Ball and Plate:
Control system simulator:
oblems/Intro00.html

28. Lab
Closed loop intro
Controlling the motor speed via on/off and PID control methods
“Loading” the motor with the blue potentiometer

29. 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