Submodule 2: Define PID and Output

Submodule 2: Define PID and Outputs

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System Key Terms

Before learning how the proportional, integral, and derivative (PID) parts of a PID controller affect a system, it is important to understand a few key terms that describe how the system behaves when trying to reach the setpoint. Click through the carousel and read each of the ten definitions. A more detailed description of proportional, integral, and derivative will be provided on the next slide.

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Check System Key Term Understanding

The next page will be a check on your system key term understanding. Drag and drop each key term to the gray box next to the appropriate definition and click the Check Answers button once you are done. The correct terms will stay in place and the incorrect terms will go back into the word bank. The Continue button will only appear once you have gotten all of the definitions correct.

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Word Bank:

Rise Time

Dampen

Tuning

Noise

Overshoot

PID Controller

Settling Time

Oscillation

Steady-State Error

Undershoot

A type of controller that continuously compares the PV to the SP and adjusts the controlled device using proportional (P), integral (I), and derivative (D) actions to minimize the error over time:

The final, persistent difference between the PV and the SP once the system reaches equilibrium:

To reduce the severity or amplitude of oscillations in the PV:

The adjustment of controller parameters to optimize system performance, minimize overshoot, and achieve desired rise and settling times:

The duration required for the PV to increase from about 10% to 90% of its final value after a change in the SP:

A repeating fluctuation of the PV above and below the SP:

Unwanted, random fluctuations in the sensor signal that can interfere with the accurate detection of the PV:

A condition where the PV temporarily exceeds the SP before stabilizing:

A condition where the PV temporarily drops below the SP before stabilizing:

The time it takes for the PV to remain within a specified tolerance range around the SP after a disturbance or SP change:

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Thank you for completing the system key term understanding check. Feel free to complete the activity again to reinforce your understanding. The next slide will show the definitions for proportional, integral, and derivative control.

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Defining P, I, and D

PID defines how the controller calculates outputs based on the error and is broken down into three parts: proportional (P), integral (I), and derivative (D). Flip each card to learn how P, I, and D signals work with a controller.

Derivative (D)

Integral (I)

Proportional (P)

Looks at the rate of change of the error and acts to speed up or slow down adjustments in the control process, typically preventing overshoot or oscillation.

Integral (I)

Proportional (P)

Derivative (D)

Adds up past errors over time to eliminate any remaining difference and reach the SP exactly.

Reacts to the current error—the greater the difference from the SP, the stronger the response.

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PID Anecdotal Examples

Derivative (D): - Bike Braking: Slowing down a bike as soon as you approach a stop sign. If you are slowing down quickly, you might ease up on the brakes to avoid stopping too early. - Connection: The derivative part looks at how quickly things are changing and takes early action to dampen any sudden movement.

Proportional (P): - Shower Temperature: If the water feels too cold, you turn the handle toward hot. The bigger the difference, the larger the adjustment. - Connection: The size of your adjustment depends directly on how far the actual temperature is from your desired comfort level—this is exactly how proportional control works.

Integral (I): - Bucket Filling: If the bucket is not filling up as quickly as you want, you start opening the tap more. - Connection: The integral part "remembers" the past difference and keeps adding effort the longer the goal is not met.

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Gain Background

Gain is a multiplier that determines how strongly each part of the PID controller reacts to the error. A higher gain makes the controller respond more aggressively, while a lower gain results in gentler adjustments. These values are represented by the symbols: - Kp: Proportional - Ki: Integral - Kd: Derivative By tuning the gain for each term, the controller adjusts how much each component influences the output, allowing for faster, slower, or more stable system responses depending on the needs of the process.

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How Gain Affects System Response

Derivative (Kd): - Use: Anticipates future error by looking at how quickly the error is changing. - Pro: Helps dampen rapid changes, making the system respond more smoothly and reducing overshoot. - Con: Excessive derivative action can amplify noise.

Proportional (Kp): - Use: Increases system responsiveness, making the control action stronger for larger errors between the SP and PV. - Pro: Can speed up reaction. - Con: Can cause overshoot or oscillations if too high.

Integral (Ki): - Use: Adds up past errors, helping the system eliminate any residual offset so the PV matches the SP exactly. -Pro: Reduces steady-state error. - Con: Too much may introduce lag or oscillations.

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PID Controller Simulator Instructions

You will now interact with a simulator that lets you experiment with how a PID controller adjusts system behavior in real-time by changing three gain sliders: Kp, Ki, and Kd. For now, use the Second Order System model because it provides a clear and balanced system response that is easy to understand and visualize when learning PID tuning. Additionally, keep the noise level at zero and ignore the IAE, ISE, and ITAE values to focus on basic PID concepts without added complexity from sensor noise and other factors.

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PID Controller Simulator Instructions

The graph shows how the system responds over time—specifically, how the PV approaches the SP based on your selected PID settings. This simulation will help you answer 12 multiple-choice questions that illustrate how changes in gain affect system behavior—key concepts for tuning effective HVAC control loops. Click the PID Controller Simulation button to open the simulation page. Set your initial SP and gain values, then click Start. If the legend overlaps the chart, zoom in or out to reposition it. Adjust the SP and gain settings as the graph develops to observe how each affects the system’s response. You can pause or reset the graph at any time. After exploring the simulation and identifying the key factors influencing system behavior, return to the slideshow to continue to the questions.

PID Controller Simulation

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PID Controller Simulator Questions

For each question, move and place the cursor icon on the answer you believe is correct. Once you are satisfied, click the Check Answer button to see if you selected the right answer. In order to advance, each question will have to be answered correctly. Additionally, once correct, a Video button linking to a short video showing a clear representation of the question will appear to the left of the Continue button. Click on it once to bring up the video and click on it again to hide it.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Ki and Kd to 0 - Set setpoint to 2 - Adjust Kp slowly from 0 to 20 while observing system response

1) How does increasing Kp affect the speed at which the system reaches the setpoint?

Has no effect

Causes the system to ignore the setpoint

Speeds up the response

Slows down the response

Increasing Kp amplifies the controller's reaction to the current error, making the system respond faster to reach the setpoint.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Ki and Kd to 0 - Set setpoint to 2 - Adjust Kp quickly from 0 to 20 while observing system response

2) What happens to overshoot and oscillation as Kp increases?

Overshoot decreases and oscillation stops

Overshoot and oscillations increase

Controller ignores the SP and produces no response

Overshoot remains the same

Higher Kp makes the controller respond more aggressively to error, which increases overshoot and can cause oscillations as the system repeatedly overcorrects.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Ki and Kd to 0 - Set setpoint to 2 - Adjust Kp from 0 to 20 while observing system response

3) What limits the system's ability to reach the setpoint when only proportional control is used?

Kd dampens the response

System cannot eliminate steady-state error without Ki

SP changes automatically over time

Controller output stops updating after startup

With Kp control alone, the system needs a remaining error to keep producing output, so it cannot fully reach the SP without Ki.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 8 and Kd to 0 - Set setpoint to 2.5 - Adjust Ki from 0 to 10 while observing system response

4) How does increasing Ki help eliminate steady-state error?

By summing all past errors to correct offset

By ignoring past errors

By delaying the response

By reducing signal noise

Ki sums past errors over time, pushing output until steady-state error disappears.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 8 and Kd to 0 - Set setpoint to 2.5 - Adjust Ki quickly from 0 to 10 while observing system response

5) What effect does high Ki have on system stability?

Can cause oscillations and overshoot

Immediately stabilizes the system

Makes system more stable and smooth

No effect on stability

High Ki can cause oscillations and overshoot due to aggressive accumulated corrections.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 8 and Kd to 0 - Set setpoint to 2.5 - Adjust Ki from 0 to 10 while observing system response

6) How does Ki influence settling time?

May increase settling time if too high

Settling time depends on the setpoint only

Has no effect on settling time

Always reduces settling time

Increasing Ki removes steady-state error, but too much Ki can cause overshoot and slow settling due to aggressive correction.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 10 and Ki to ~1 - Set setpoint to 1.5 - Set Kd to 0 and observe system response. Reset, set Kd to 10, and observe system response again.

7) How does increasing Kd affect overshoot and settling time?

Always reduces overshoot and settling time

May increase overshoot and settling time if too high

Has no effect on settling time

Has no effect on overshoot

Kd dampens sudden changes; reduces overshoot and speeds settling.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 10 and Ki to ~1 - Set setpoint to 1.5 - Set Kd to 0 and observe system response. Reset, set Kd to 10, and observe system response again.

8) Can Kd reduce oscillations caused by high Kp or Ki?

Yes

Only if Ki is zero

No

Only if Kp is zero

Yes, derivative action counters rapid changes to reduce oscillations.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 10 and Ki to ~1 - Set setpoint to 1.5 - Set Kd to 0 and observe system response. Reset, set Kd to 10, and observe system response again.

9) What happens when Kd is too large?

System may become noisy or unstable

Always improves system stability

Makes system slow without oscillation

No noticeable effect

When Kd is set too high, the controller overreacts to rapid changes in the signal, amplifying noise and causing unstable system behavior.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 8, Ki to ~2, and Kd to ~1 - Start with setpoint at 1 and do a sudden change to 3 while observing system response

10) How quickly does the system respond to the setpoint change?

Depends on the gain settings

System never reaches the setpoint

Always very slow

Instantly

Response speed depends on gain settings that control reaction aggressiveness.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 8, Ki to ~2, and Kd to ~1 - Start with setpoint at 1 and do a sudden change to 3 while observing system response

11) Are there oscillations or overshoot after the change?

Yes, if gains are not tuned well

No oscillations or overshoot ever

Only overshoot, no oscillations

Both depend on setpoint only

Oscillations/overshoot happen if gains are too high or poorly tuned.

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PID Controller Simulator Questions

Use the following simulation settings for this question: - Set Kp to 8, Ki to ~2, and Kd to ~1 - Start with setpoint at 1 and do a sudden change to 3 while observing system response

12) How do gain values help smooth or speed up the response?

Proper tuning balances speed and smoothness

Gains control only steady-state error

Gains have no effect on system response

Higher gains always smooth response

Proper tuning balances gains for smooth and fast response without instability.

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