electronic (pid) controllerskamran/ee3202/lab9/pidlablecture.pdf · pid controllers can use all 3...

Electrical / Computer / Telecommunications Engineering

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Electronic (PID) Controllers



Outline of LectureControl System BasicsPID ControllersPreparation for the HW and Lab.



Control System BasicsTo prepare for this lab, you must watch the Matlab “Tech Talk” Videos by Brian

Douglas. These are light on math and heavy on intuition. Part 1: https://www.mathworks.com/videos/understanding-pid-control-part-1-what-is-pid-

control--1527089264373.html

Part 2: https://www.mathworks.com/videos/understanding-pid-control-part-2-expanding-beyond-a-simple-integral-1528310418260.html

Part 3: https://www.mathworks.com/videos/understanding-pid-control-part-3-expanding-beyond-a-simple-derivative-1531120808026.html

Suggestion: Listen on 1.5x speed and watch carefully.

https://www.mathworks.com/videos/understanding-pid-control-part-1-what-is-pid-control--1527089264373.html

https://www.mathworks.com/videos/understanding-pid-control-part-2-expanding-beyond-a-simple-integral-1528310418260.html

https://www.mathworks.com/videos/understanding-pid-control-part-3-expanding-beyond-a-simple-derivative-1531120808026.html



Control System Basics – cont’d Controllers have a single purpose: Make our lives easier and better. Keep a system (and/or a subsystem) at an optimal setting so that a human being doesn’t have

to monitor it continuously.

Electronic Controllers are used in myriad applications: Set and maintain temperature … in your oven and in your home. Maintain the speed of your car. (cruise control, fuel to air ratio, spark timing, temperature, etc.) o Autonomous vehicles use more: directional, collision avoidance, parallel park, etc.

Read-write head positioning in hard drives Power plants and the voltage level coming into your home. Specialty controllers enable pilots to fly enormous and complex aircraft. Nearly every manufacturing process today (and all Robotics) etc.

An Uncontrolled system = “Open Loop” system (no “feedback” of info).



Control System Basics – cont’d The most common analog controller is called a “PID-Controller” where: “P” = “Proportional”, “I” = “Integral”, “D” = “Derivative”.

All PID-Controllers use an “error signal” e(t) e(t) ≡ (Desired Performance – Actual Performance). Goal is to make e(t) = 0 and then keep it there.

The PID Controller uses e(t) in 3 fashions: “P” uses e(t) directly This is equal to the present performance. “I” uses ∫ e(t) dt This is related to past performance. “D” uses d(e(t)) / dt This enables a prediction of future performance.

Goal: P, I and D go to zero and remain there. (e(t), ∫ e(t) dt, and d(e(t)) / dt)



Control System Basics – cont’d Suppose we have a error signal, e(t) as plotted. “P” is the Present value of e(t). “I” is the area under the e(t) curve o Gives information on the past values of e(t).

“D” is the slope of the e(t) curve o Enables one to predict future values of e(t).

This is why P, I and D should all go to zero! Present error should be zero (at the correct output) After reaching e(t) = 0, ad staying there, the area under the e(t)

curve should go to zero too. (Note that this takes some time.) When e(t) = 0, we want it to stop changing in time. Thus, the

derivative of e(t) should go to zero as well.

~

I

P

D

0

e(t)

timePresent



Control System Basics – cont’d PID Controllers can use all 3 or a subset of the 3 You will build a P-Controller in Lab. o “P” Controllers can function well in certain circumstances.o Must always have the “P” in any controller. “P” gives direct e(t) information & is easiest to implement. I-, D- and ID-Controllers are NOT used. (Don’t function well.) I-Controllers are slow and oscillate. D-Controllers are plagued by noise and cannot know if

they made it to the correct output! ID-Controllers can bring the worst of both worlds …

PI-Controllers are very widely used. PD-Controllers are rare, but possible. PID controllers are also widely used.

~

I

P

D

0

e(t)

timePresent



Control System Basics – cont’d What does “open loop” operation look like? Two exampleso Baked Muffins (= Output): “System-Setting Input” = Oven Power (Heater); “Input” = Muffin Dough

o Automobile Speed: “System-Setting Input” = Fuel Injector Timing; “Input” = Fuel

There is a problem here: o No measurement of the output. (Muffins, Speed) o Therefore, no control of the output “quality”.

Somehow, a measurement of the output must influence the “System-Setting Input” ! (FEEDBACK)

Out

putA System –

It does something.

SystemSetting

System-Setting Input

Input



Control System Basics – cont’d What does “Closed Loop” operation look like? Two examples of FEEDBACK: o Baked Muffins (= Output): “System-Setting Input” = Oven Power (Heater); “Input” = Muffin Dough “Output Signal” = Muffin Color

Muffins under-baked? Turn up the oven. o Automobile Speed: “System-Setting Input” = Fuel Injector Timing; “Input” = Fuel “Output Signal” = Speed

Going too fast? Reduce the fuel input. Output Sensor

DesiredOutputSignal

Output Signal

Out

putA System –

It does something.

SystemSetting

System-Setting Input

Input

Q: What does the connection between “Desired Output Signal”, “Output Signal” and the “System-Setting Input” look like?

A: PID-Controller.



Control System Basics – cont’d A PID-Controller compares the “Desired Output Signal” and “Output Signal” to

derive the right “System-Setting Input”. A simplified schematic is shown below.

Out

putA System –

It does something.

SystemSetting

Output Sensor

DesiredOutputSignal

P: 𝐾𝐾𝑝𝑝𝑒𝑒 𝑡𝑡 →

Σ–

+ Difference “Error” 𝑒𝑒 𝑡𝑡

I: 𝐾𝐾𝑖𝑖 ∫𝑡𝑡−𝛼𝛼𝑡𝑡 𝑒𝑒 𝜏𝜏 𝑑𝑑𝜏𝜏 →

D: 𝐾𝐾𝑑𝑑 �𝑑𝑑𝑒𝑒 𝑡𝑡𝑑𝑑𝑡𝑡 →

Σ+

+

+

Input

PID Controller

Output Signal

Note: Represents

a Voltage summing point.

Σ



Examining the PID-ControllerWhat do the Electronics of a PID-Controller look like? Effectively – Op Amps. o Σ = Differencing (Summing) Op Ampo P = Non-Inverting Op Ampo I = Integrating Op Ampo D = Differentiating Op Amp …

(But see the Matlab Tech Talk) Digital PID-Controllers can work well. o ADC + Program + DAC + Buffer Amp.

You will build an analog P-Controller It is one Differencing (Summing) Op Amp!

DesiredOutputSignal


Σ–

+ Difference “Error” 𝑒𝑒 𝑡𝑡 I: 𝐾𝐾𝑖𝑖 ∫𝑡𝑡−𝛼𝛼

𝑡𝑡 𝑒𝑒 𝜏𝜏 𝑑𝑑𝜏𝜏 →


Σ+

+

+

PID Controller

Output Signal

P: 𝐾𝐾𝑝𝑝𝑒𝑒 𝑡𝑡 →Σ–

+ Difference “Error” 𝑒𝑒 𝑡𝑡 Vo = Kp e(t)



Differencing Op Amp as a P-Controller: You have worked with Difference Op

Amps before. (Fund. #1) Upper diagram corresponds to the

lower schematic using an OPA551 op amp.

This Lab uses an OPA551 (by TI). Larger Voltage Capability (± 30V) Larger Current Capability (200mA) o Motors require larger currents

Fully Protected:o Thermal Shutdown o Output Current-Limited

See the datasheet.

Desired Output Signal

Output Signal

-15V

Unity Gain Difference Amp

VoVm

0.1uF

++

-

OPA551

Rf 10k

R3 10kR1 10k

0.1uF

Vp

R4 10k

+15V

Vo = Kp e(t)

P: 𝐾𝐾𝑝𝑝𝑒𝑒 𝑡𝑡 →Σ–

+ Difference “Error” 𝑒𝑒 𝑡𝑡 Vo = Kp e(t)

+

–



Lab ObjectivesHardware Level Understanding of PID-Controllers. Ability to design, build and test a Proportional Controller (P-Controller). What you will do in Lab: 1. Measure the Vin-Vout characteristic of a coupled pair of P711A toy motors for

two different load impedances. 2. Build and test a P-Controller for the two-motor system using a Differencing Op

Amp with two levels of gain (1x and 10x) and compare performance. 3. Measure the time response of the coupled motor system to a step change in

the input using the 10x gain level.



Lab BackgroundElectric Motors can also serve as electric generators: Two coupled motors simulates (poorly) a wind turbine or other electric generator. o Driver Motor spins the rotor of the Generator Motor → Electricity Below a Threshold Input Voltage: The driver motor does not spin → No Output Voltage.

Above the Threshold Input Voltage: Increasing Input Voltage → Faster driver motor spin rate → Increasing Output Voltage

Driver Motor Generator Motor

Output Voltage

(Opposite polarity of input voltage)

Input Voltage

Rotor Coupling



Lab Background Cont’d.Driver motor spins the rotor of the Generator motor → Very Noisy EMF! Motor spin produces spikes in EMF having a DC average. o You could choose to examine this more in depth during the lab (not required). Are the spikes consistent? Repeatable? Do they vary with Driver Motor Speed? Etc. Do the spikes (if not reduced) affect the P-Controller?

Use a large (>= 100 uF) shunt capacitor on both motors to: o reduce high frequency noise and retain the DC component of the Output Voltage.

Driver Motor Generator Motor

Output Voltage

(Opposite polarity of input voltage)

Input Voltage

Rotor Coupling



Lab Procedure: Make open loop measurements to compare with

P-Controller measurements: Obtain the open loop Vout – Vin characteristic with: o No load resistor across the generator-motor output,o A 100 Ohm load resistor

Note how the load resistor changed the characteristic.

A example Vout – Vin characteristic (no load resistor). The one obtained in lab should be

similar except fewer data-points.

Out

putGenerator-

MotorDriver Motor

Output SensorGenerator Motor Output Voltage – Vout

Load: ZL

Driver Motor Input Voltage – Vin



Lab Procedure: Build and test a unity gain (Kp = 1) P-Controller: Build using the OPA551PA and 10k Ohm resistors. Test BEFORE connecting to your motors! (Must be sure

that it is indeed outputting the correct difference in voltage between the two inputs, “Vp” and “Vm”.)o Vo = Vp – Vm

Once the difference amp is working: Connect it to your motors. o Driver Motor Input Voltage = Vo = Kp e(t)o Generator Motor Output Voltage = Vm

o Desired Output Voltage = Vp

Make sure that the generator motor output is the same polarity as the driver motor input!

-15V

Unity Gain Difference Amp

VoVm

0.1uF

++

-

OPA551

Rf 10k

R3 10kR1 10k

0.1uF

Vp

R4 10k

+15V

Vo = Kp e(t)+

–



Lab Procedure Cont’d Your system will be like this schematic.

Out

putGenerator-

MotorDriver Motor

Output Sensor

DesiredOutputVoltage


Σ–




Σ+

+

+

P Controller

Generator Motor Output Voltage

Load: ZL

Driver Motor Input Voltage



Lab Procedure Cont’d Measure the system performance using the unity gain P-Controller: Obtain the Vout – Desired Output Voltage (DOV) characteristic with: o No load resistor across the generator-motor output,o A 100 Ohm load resistor as load

Did the P-controller cause Vout = DOV? Why or why not? Compare to the open loop case: o Did the P-controller cause the output values, Vout, to change less with load? Why or why not?

Measure the system performance using the 10x gain P-Controller: Build the 10x gain difference amplifier and be sure that Vo = 10*(Vp – Vm) before using it as the P-

controller. Measure the Vout - DOV characteristic again, o with no load and o with the 100 Ohm resistor as load.

Did the P-controller cause Vout = DOV? Why or why not? Compare to the open loop and 1x gain cases: o Did the 10x gain P-controller cause Vout to change less with load? Why or why not?



Lab Procedure Final Measure Vout(t) response using a Square-Wave

Input as DOV(t) Capture both DOV(t) and Vout(t) on the Oscilloscope. o Does Vout follow DOV in time? o Measure the Vout “rise time” (10% to 90%) and “fall

time” (90% to 10%) . o Speculate on any potential causes for these rise and

fall times. What aspects of this system are most likely to cause a slowed response or a delayed response?

How might one reduce the “rise time” and “fall time”? Test your hypotheses and report on at least one. Example oscilloscope traces for DOV(t) – Yellow,

Vout(t) – Green and Trigger Sync. – Blue .



HW Help (Examples to help you with the HW problems)Prb 1: Watch the Matlab Tech Talks. Prb 2: Use the Vout - Vin characteristic curves.

a) Find the steady state operating points when DOV = 4 V, for both the 1 MOhm and 50 Ohm loads in an:

o Open Loop System, o A 1x gain P-Controller System, and o A 10x gain P-Controller System.

b) Compare the [1] open loop, [2] 1x gain and [3] 10x gain P-Controller Systems.

o Which system gets Vout closest to DOV? o Which system keeps Vout closest to a constant value as

the load is changed from 1 MOhm to 50 Ohms?



HW Help Cont’dFrom the graph: For 1 MOhm Load: 𝑉𝑉𝑜𝑜𝑜𝑜𝑡𝑡 = 𝑎𝑎 ∗ 𝑉𝑉𝑖𝑖𝑖𝑖 + 𝑏𝑏 = 0.81 ∗ 𝑉𝑉𝑖𝑖𝑖𝑖 − 0.68, 𝑎𝑎 = 0.81, 𝑏𝑏 = −0.68 For 50 Ohm Load: 𝑉𝑉𝑜𝑜𝑜𝑜𝑡𝑡 = 𝑎𝑎 ∗ 𝑉𝑉𝑖𝑖𝑖𝑖 + 𝑏𝑏 = 0.41 ∗ 𝑉𝑉𝑖𝑖𝑖𝑖 − 0.22, 𝑎𝑎 = 0.41, 𝑏𝑏 = −0.22Open Loop: Use the above equations directly because Vin = DOVP-Controllers: Now 𝑉𝑉𝑖𝑖𝑖𝑖 = 𝐾𝐾𝑝𝑝 ∗ 𝐷𝐷𝐷𝐷𝑉𝑉 − 𝑉𝑉𝑜𝑜𝑜𝑜𝑡𝑡 = 𝐾𝐾𝑝𝑝 ∗ 𝑒𝑒 𝑡𝑡

A little algebra gives: 𝑉𝑉𝑖𝑖𝑖𝑖 = 𝐾𝐾𝑝𝑝∗ 𝐷𝐷𝐷𝐷𝐷𝐷−𝑏𝑏1+𝑎𝑎∗𝐾𝐾𝑝𝑝

and 𝑉𝑉𝑜𝑜𝑜𝑜𝑡𝑡 = 𝑎𝑎∗𝐾𝐾𝑝𝑝∗𝐷𝐷𝐷𝐷𝐷𝐷+𝑏𝑏1+𝑎𝑎∗𝐾𝐾𝑝𝑝

Given DOV = 4 V 1 MOhm 50 Ohm Percentage Variation with Load

Open loop: Vout = 2.6 V 1.4 V 45% = (2.6-1.4)/(2.6) 1x gain: Vout = 1.4 V 1.0 V 29% = (1.4-1.0)/(1.4) 10x gain: Vout = 3.5 V 3.2 V 9% = (3.5-3.2)/(3.5)



HW Help FinalPrb 4: Design a P-Controller for your dual motor experiment. Spend time designing the layout and connections of your P-Controller. o Use the OPA 551 and layout the connections in PSPICEo Are you able to simulate it?

Questions?



Extras



Lab – cont’d

Out

putGenerator-

MotorDriver Motor

Output Sensor

DesiredOutputVoltage


Σ–




Σ+

+

+

PID Controller

Generator Motor Output Voltage

Load: ZL

Driver Motor Input Voltage

electronic (pid) controllerskamran/ee3202/lab9/pidlablecture.pdf · pid controllers can use all 3...

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