EET273

1. EET273 Electronic Control Systems II Week 10 – Final Review

2. Control Terminology • Process/Plant – the physical system we wish to monitor and control • Process Variable (PV) – output variable to be controlled • Setpoint(SP) – input to the system, the desired value of the PV • Controller – module that processes system error and drives the plant • Final Control Element (FCE) – actuator that is acting on the process • Manipulated Variable (MV) or Output – Controller output variable that manipulates the plant • Open Loop – no feedback from output to input • Closed Loop – with feedback from output to input

3. Ladder Logic • Circuits are connected between 2 “rails”, and listed from top to bottom in “rungs”, resembling a ladder. • L1 – “hot” AC wire, L2 – “neutral” or grounded wire • All electrically common points are numbered with the same number (and preferably the same color wire, though not always practical) • Fuses are connected to the left rail • Ground fault to center wire causes fuse to blow • Switches are placed on the left rail of the diagram • Loads are placed on the right rail of the diagram (grounded side) • In case of a ground fault, both sides of the load are grounded

4. PLCs • Why PLCs? • Convenient alternative to relays • Instead of re-wiring a circuit, just load a new PLC program • May be programmed using a ladder logic diagram • Makes existing hardware more versatile: • Have a NO switch, but need a NC switch? Just switch the behavior of X1 in the PLC • “Virtual switches” in the PLC allow a physical switch to used multiple times in different rungs of the PLC ladder logic • Real-time remote monitoring and control via software

5. Proximity Switches • Because proximity switches are active, they typically do not have simple switch terminals like a passive switch would. Instead they either source or sink current • Sinking – sensor sinks current from circuit, NPN type, “low-side” • Source – sensor sourcing current to circuit, PNP type, “high-side” • Notice that emitter is always connected to power rail – common emitter config

6. Switching Example • LED in this circuit will turn on if the liquid level rises above 14 inches AND the pressure falls below 22 PSI AND either the flow is less than 3 gallons per minute OR the temperature is greater than 125°F. • 22 psi sensor (NC) is detecting a LOW pressure state, which is the normal state, but not the desired (or typical) state • Similarly, the 3 GPM sensor (also NC) is detecting LOW flow

7. On-delay & Off-delay Relays • On delay relays: delay occurs when coil is energized, no delay when coil is de-energized • Off delay relays: delay occurs when coil is de-energized, no delay when coil is energized • Arrow in symbol represents when delay occurs • Up: energized • Down: de-energized • Can be either NO or NC

8. On-delay & Off-delay Relays Normally open, timed-close Normally open, timed-open

9. 4–20mA signaling • Most popular form of signal transmission in modern industrial systems • An analog signaling standard • An analog signal is “mapped” to a current range of 4mA – 20mA • 4mA • lowest possible signal level • 0% of scale • 20mA • highest signal level • 100% of scale

10. Voltage vs. Current signaling

11. 4–20mA signaling • Mapping a 50 - 250°C temperature scale to 4 – 20mA • 50°C  4mA • 250°C  20mA

12. 4–20mA signaling example

13. Solving using a linear equation • Use y = mx + b  calculate slope, calculate y-intercept • For input: 0-350 GPM output: 4-20 mA

14. Calibration Errors Zero shift   Span shift

15. Calibration Errors – Linearity errors • Linearity error • The response of an instruments function is no longer a straight line • Cannot be fixed by a zero/span correction, because the response is no longer a linear function • Some instruments offer a “linearity” adjustment, which must be carefully adjusted according to the manufacturer instructions • Often the best you can do is “split the error”, finding a happy medium between error high and low extremes

16. Calibration Errors – Hysteresis errors • Instrument responds differently to an increasing input compared to a decreasing input • This type of error can be detected by testing the instrument going up through the range, then down through the range • Typically caused by mechanical friction • Cannot be rectified through calibration, typically must replace the deflective component

17. 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

18. 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

19. 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%

20. 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

21. 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

22. 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

23. 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)

24. Controllers • Error is: the different between the system input (SP) and output (PV) • The purpose of feedback is to reduce system error • The purpose of a controller to process the system error in such a way that it reduces error quickly and efficiently • Proportional controllers work by multiplying the error by some scaling constant , this is fairly effective but has limitations (creates offset and/or overshoot)

25. 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

26. 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

27. PID Control • P – Proportional • I – Integral • D – Derivative • A controller can consist of 1 or more of these elements together, depending on the type of system/performance required • P controller • PI controller • PD controller • PID controller • We can use multiple types of controllers in parallel, and sum the outputs of each controller

28. Integral Controllers • For our purposes, the word “integral” can be used interchangeably with “accumulated sum” • An integral controller accumulates the error over time • If there is any steady state error in a system, the integral controller will continue to accumulate this error, and eventually drive it to zero • Because integral controllers only operate on accumulated changes in error, they are slower to respond to error than a proportional or derivative controller

29. Derivative Controller • While a proportional (P) controller is looking at the actual value of the system error, a derivative controller is looking at the slope of the error • Error is increasing quickly lots of derivative control • Error is stable  very little derivative control • The amount of derivative control is set by the constant , (or )

30. Derivative Controller • Differential controllers are often used to respond to quick changes in error, and prevent the error from changing too quickly • This can help reduce overshoot coming from the P or I controller • Since the D controller is “keeping an eye out” for sudden changes, we can “get away with” more P and I than we could otherwise (and still avoid overshoot) • Since D controllers respond to the error’s rate of change, they are more susceptible to high frequency noise – so be careful when implementing them!

31. PID Control • Proportional: • Reacts to error in the present • Good for performing the bulk of error reduction • Results in “proportional-only offset”, which can reduced, but never eliminated with proportional only control • Integral: • Reacts to error in the past • Excellent at removing steady state errors • Slow to respond due to time needed to accumulate error • Derivatives: • Reacts to error in the future (anticipates error by looking at slope) • Starts working when error is changing quickly • Stops working when error is constant • Not good at eliminating steady state errors – if error is constant, D controller doesn’t care

32. PID Control

33. PID controllers – different configurations • P: Removes bulk of error, will always have offset (in a loaded system) • I: Completely removes offset (eventually), slower response • PI: Removes error quickly, and eliminates offset, may overshoot • PD: Removes bulk of error, D corrects for overshoot, will have offset • PID: Completely removes offset, responds quickly, D corrects for overshoot

34. Final Exam • The Final – Monday 6/10 – 8pm: • 60%: Closed loop control, On/Off Control, PID control • Look at SP/PV graphs, design a basic control strategy, use On/Off, P, PI, or PID? • Look at SP/PV graphs, determine which P/I/D constants might need tuning • Identify control elements, PV, SP, MV, etc. • 20%: Signaling/calibration • 20%: Ladder logic, relays, switching/sensors • Two pages of notes allowed • You may use a calculator • You should study: • HW’s, quizzes, midterm, final review sheet

35. Notes • Highly recommend playing with the Matlab/Octave PID simulator • Final review sheet is posted online under HW section – you do not need to turn this in