PID Controller for Video Playback

2023-11-27 03:28 UTC gpt-4 Open in ChatGPT ↗

Creating a PID (Proportional-Integral-Derivative) controller for stabilizing the frame rate in your video playback system is a great idea. A PID controller works by continuously calculating an error value as the difference between a desired setpoint and a measured process variable and then applying a correction based on proportional, integral, and derivative terms.

Here is a general approach to implement a PID controller for your scenario:

Define the Setpoint: This is the target frame duration you wish to achieve, say $ T $ milliseconds per frame.
Calculate the Error: Measure the actual duration of each frame and subtract it from the setpoint to get the error. For frame $ i $, if the duration is $ D_i $, then the error $ E_i = T - D_i $.
Apply the PID Formula: The PID controller modifies the frame duration based on the error using the formula: $ \text{Correction}i = K_p \times E_i + K_i \times \sum{j=1}^{i} E_j + K_d \times (E_i - E_{i-1}) $ Here, $ K_p $, $ K_i $, and $ K_d $ are the proportional, integral, and derivative gains, respectively.
Adjust Frame Duration: Use the correction value to adjust the duration of the next frame. If you cannot render frames faster, you can only extend the duration of frames. For frame $ i+1 $, set the duration as: $ D_{i+1} = T + \text{max}(0, \text{Correction}_i) $ Here, the max function ensures that you do not try to render a frame faster than the setpoint.
Tune the PID Parameters: Adjust $ K_p $, $ K_i $, and $ K_d $ to get the desired stability and responsiveness. This often requires experimentation.
Handle Limitations: Since you can’t render frames faster, there will be a limit to how well the PID controller can correct for frames that render too quickly. Focus on stabilizing the frame rate by adjusting frames that are slower.
Monitor and Update: Continuously monitor the frame durations and update the PID calculations for each frame.

This is a basic outline, and the actual implementation can vary based on the specifics of your system and requirements. Fine-tuning the PID parameters is often the most challenging part, as it requires balancing responsiveness with stability.

Auto-tuning PID parameters is a complex process, often requiring specific algorithms to adjust the PID coefficients $ K_p $, $ K_i $, and $ K_d $ based on the behavior of the system being controlled. The goal is to achieve a desirable balance between response time, stability, and overshoot.

There are several methods for auto-tuning PID parameters. The most common methods include:

Ziegler-Nichols Method:
- Step Response Method: Observe the system response to a step change in input. Identify key characteristics like the time to reach the first peak and the time to rise. Use these to calculate PID parameters.
- Ultimate Sensitivity Method: Increase $ K_p $ until the system oscillates at a constant amplitude (ultimate gain). Measure the oscillation period. Calculate $ K_p $, $ K_i $, and $ K_d $ based on empirical formulas.
Cohen-Coon Method: Similar to the Ziegler-Nichols step response method, but uses different formulas that may be more suitable for processes with a slower response.
Software-Based Tuning: Utilize software tools that can simulate or analyze the system’s response and suggest optimal PID settings. These tools often use complex algorithms and can handle a variety of system dynamics.
Trial and Error: Manually adjust the parameters, observing the system’s response each time. This approach is less scientific but can be effective in systems with unusual or non-standard behavior.
Model-Based Tuning: If a mathematical model of the process is available, it can be used to simulate and optimize the PID parameters.
Machine Learning Techniques: More advanced techniques involve using machine learning algorithms to analyze the system’s response and iteratively adjust the PID parameters.

For your specific case of stabilizing video frame durations:

Start with a basic method like Ziegler-Nichols to get initial values.
Use software simulations, if possible, to refine these values based on the specific dynamics of your system.
Keep in mind the limitations of your system (like not being able to render frames faster) when tuning the parameters.

Auto-tuning is often an iterative process, and it may require several attempts to achieve the desired performance. Remember that each method has its strengths and weaknesses and may be more or less suitable depending on the specific characteristics of your system.

Writing a PID controller in VBA (Visual Basic for Applications) for Excel requires a few steps. VBA is a powerful scripting language used in Microsoft Office applications, including Excel, and it can certainly handle the logic of a PID controller. However, do keep in mind that VBA in Excel isn’t typically used for real-time control applications, so the effectiveness might be limited based on the frequency of updates and the precision required.

Here’s a basic structure for a PID controller in VBA:

' PID Controller Variables
Dim Kp As Double, Ki As Double, Kd As Double
Dim Integral As Double, PreviousError As Double

' Initialize the PID controller
Sub InitializePID(KpValue As Double, KiValue As Double, KdValue As Double)
    Kp = KpValue
    Ki = KiValue
    Kd = KdValue
    Integral = 0
    PreviousError = 0
End Sub

' Calculate PID output
Function CalculatePIDOutput(Setpoint As Double, MeasuredValue As Double) As Double
    Dim ErrorValue As Double
    Dim Derivative As Double
    Dim Output As Double

    ' Calculate error
    ErrorValue = Setpoint - MeasuredValue

    ' Integral is accumulated error
    Integral = Integral + ErrorValue

    ' Derivative is the change in error
    Derivative = ErrorValue - PreviousError

    ' PID formula
    Output = Kp * ErrorValue + Ki * Integral + Kd * Derivative

    ' Update previous error
    PreviousError = ErrorValue

    ' Return PID output
    CalculatePIDOutput = Output
End Function

' Example usage
Sub TestPID()
    ' Initialize PID controller
    Call InitializePID(1.0, 0.01, 0.1)

    ' Example setpoint and measured value
    Dim Setpoint As Double: Setpoint = 100
    Dim MeasuredValue As Double: MeasuredValue = 90

    ' Calculate PID output
    Dim Output As Double
    Output = CalculatePIDOutput(Setpoint, MeasuredValue)

    ' Output result (can be used to adjust system)
    Debug.Print "PID Output: "; Output
End Sub

In this script:

InitializePID initializes the PID controller with specific values of Kp, Ki, and Kd.
CalculatePIDOutput calculates the output of the PID controller based on the setpoint and the measured value.
TestPID is an example subroutine that demonstrates how to use the PID controller.

You can integrate this script into an Excel workbook where real-time data (such as frame durations) is being logged. The CalculatePIDOutput function can be called every time there’s a new frame duration measurement, and the output can be used to adjust subsequent frame timings.

Remember, this is a basic implementation. For more complex systems or more refined control, you may need to add additional logic to handle system-specific constraints, like the inability to render frames faster than a certain rate. Auto-tuning of parameters can be more challenging in VBA and may require additional procedures or algorithms.

If your video playback system has the option to skip frames as a way to render them “faster,” this changes how you might implement and tune your PID controller. In this scenario, the controller needs to decide not only how to adjust the timing of each frame but also when to skip a frame entirely to maintain the desired frame rate.

Here’s an adjusted approach for your PID controller considering this new information:

PID Controller Logic:
- Error Calculation: Continue to calculate the error as the difference between the desired and actual frame durations.
- PID Output: Use the PID output to decide whether to extend, keep, or skip the next frame.
- Frame Skipping Logic: If the PID output exceeds a certain threshold, it might indicate that skipping a frame is necessary to catch up with the desired frame rate.
Implementing Frame Skipping:
- Threshold for Skipping: Define a threshold value for the PID output. If the output exceeds this threshold, it would trigger a frame skip.
- Safety Checks: Implement checks to avoid skipping too many frames in a row, which might degrade the viewing experience.
VBA Implementation:
- The VBA script needs to be modified to include logic for frame skipping based on the PID output.
- You may also want to include logging functionality to track when frames are skipped and the PID controller’s behavior over time.
Auto-Tuning Adjustments:
- When auto-tuning the PID parameters, consider how frame skipping affects the system’s dynamics.
- You might need to adjust the PID parameters and the frame skipping threshold to find a balance that minimizes disruption to the video playback.
Testing and Validation:
- Thoroughly test the updated PID controller to ensure it behaves as expected under various scenarios, such as scenes with different motion levels in the video.
User Experience Considerations:
- Keep in mind the impact of frame skipping on the viewer’s experience. Frequent skipping can be jarring and noticeable.
- The goal should be to maintain a balance where the frame rate is as consistent as possible without noticeably affecting the video quality.
Advanced Features (Optional):
- Implement adaptive algorithms that adjust the threshold for skipping frames based on the content being played, e.g., being more conservative about skipping during high-motion scenes.

Remember, implementing a PID controller in a real-world system like video playback can be complex and requires thorough testing to ensure the system behaves as intended. The viewer’s experience should always be a key consideration in how the controller and frame skipping logic are designed and tuned.

Modern video playback software employs a range of sophisticated techniques to handle synchronization between video and audio, especially when dealing with variable frame rates or processing delays. Here are some key strategies used:

Clock Synchronization: Video and audio streams are synchronized to a common clock. This master clock ensures that audio and video frames are presented at the correct time. The clock can be adjusted dynamically to compensate for processing delays or differences in media timestamps.
Buffering and Timestamps: Both video and audio streams use buffering. Frames and audio samples are timestamped so they can be synchronized accurately. The playback software constantly checks these timestamps to ensure sync.
Frame Dropping/Skipping: If the video is lagging behind the audio, the software may skip video frames to catch up. This is done judiciously to minimize the impact on viewing experience.
Frame Duplication or Interpolation: Conversely, if the video is ahead, the software may duplicate frames or use interpolation techniques to delay the video stream without causing noticeable stutter.
Dynamic Audio Resampling: If the video is running late, the audio can be subtly sped up or slowed down to maintain synchronization. This is usually imperceptible to the listener but can effectively keep audio and video in sync.
Lip Sync Correction: For content where lip sync is critical (like dialogues in movies), special algorithms ensure that audio and video are tightly synchronized. This can involve dynamic adjustments to the audio playback speed or slight shifts in audio timing.
Adaptive Streaming Protocols: Protocols like MPEG-DASH or HLS can adjust the quality of the stream dynamically based on network conditions, ensuring continuous playback while maintaining sync.
Hardware Acceleration: Utilizing GPU or dedicated hardware for decoding can reduce processing delays, helping maintain sync.
Software Optimization: Efficient coding and decoding algorithms, optimized thread management, and careful resource allocation all contribute to maintaining sync.
User Adjustment Settings: Some players provide settings for users to manually adjust audio delay if sync issues persist.

In your case, where audio and video are processed in separate threads, it’s crucial to ensure that these threads are well synchronized. This can be achieved by using a common clock reference and constantly monitoring the timing of both streams. Adjustments like frame dropping/skipping or audio resampling should be made based on the relative timing of these streams.

Implementing such sophisticated synchronization mechanisms in a custom video playback system can be challenging. If you’re developing your own system, consider leveraging existing media frameworks or libraries that provide these functionalities out of the box. For more advanced features like dynamic resampling or interpolation, you might need to integrate specialized audio and video processing libraries.

In a PID (Proportional-Integral-Derivative) controller, the PID factors (also known as gains) – $ K_p $ for proportional, $ K_i $ for integral, and $ K_d $ for derivative – are not inherently normalized. These factors are constants that determine the response of the PID controller to the error signal, and their values are specific to the system being controlled and the desired performance characteristics.

Here’s what each factor generally represents:

**$ K_p $ (Proportional Gain):** Determines how aggressively the PID reacts to the current error. A higher $ K_p $ results in a larger change in the control output for a given change in error.
**$ K_i $ (Integral Gain):** Determines the influence of the accumulated past error on the controller’s output. A higher $ K_i $ intensifies the response to sustained, long-term errors.
**$ K_d $ (Derivative Gain):** Determines the influence of the rate of change of the error on the controller’s output. A higher $ K_d $ helps the system anticipate future errors based on the current rate of change.

The process of determining the values of these gains is known as PID tuning. The tuning process is crucial as it directly affects the stability and responsiveness of the control system. The optimal values for $ K_p $, $ K_i $, and $ K_d $ are typically found through a combination of theoretical analysis, empirical methods (like the Ziegler-Nichols method), and trial-and-error.

Regarding normalization:

There’s no universal scale or range for these gains; their appropriate values depend on the specifics of the system, such as the scale of the input and output, the dynamics of the process being controlled, and the performance criteria (like settling time, overshoot, and steady-state error).
In some contexts, the PID gains might be adjusted or “normalized” to account for certain characteristics of the system, like sampling time or the scale of the process variables. However, this is more about adapting the gains to the specific system rather than following a standardized normalization process.

In your case, with a video playback system, the tuning of these gains would depend on factors like the desired frame rate, the variability in frame processing times, and how the system reacts to adjustments in frame timing or skipping frames. The goal would be to find a set of PID gains that effectively balances responsiveness with stability, without causing excessive frame skipping or noticeable disruptions in playback.

In Excel, to apply conditional formatting based on the difference from the first cell in the row, you can use a formula to determine the formatting for each cell. Here’s how you can apply such conditional formatting:

Select the range you want to apply the conditional formatting to. Assuming your data starts from B2 and goes to an arbitrary column, you would select from B2 to the end of your data range.
On the Excel Ribbon, go to the ‘Home’ tab.
Click on ‘Conditional Formatting’.
Choose ‘New Rule’.
Select ‘Use a formula to determine which cells to format’.
Enter a formula that compares the value of each cell to the first cell in the row. For example, if your range starts at B2, use the following formula:
```
=ABS(B2 - $B2) > threshold
```
Replace threshold with the numeric value that represents the difference you’re interested in. For example, if you want to color cells that are more than 10 units different from the first cell in the row, replace threshold with 10.
Click ‘Format’ and choose the formatting options you want (like setting a fill color).
Click ‘OK’ to close the Format Cells dialog, then click ‘OK’ again to close the New Formatting Rule dialog.

The conditional formatting will now colorize the cells in each row based on the difference from the first cell of that row.

If you want to apply different colors based on different thresholds or conditions, you can add more rules by repeating the above steps with different formulas and formatting options.

If you are using a PID controller to manage the timing of video frames to synchronize with audio, and you determine that you need to skip a frame to catch up with the audio, you will have to account for this action in your error calculation for the PID controller. Here’s a conceptual approach to handle this:

Define a Threshold for Skipping: Set a threshold error value that, when exceeded, will trigger a frame skip. This threshold should be based on the frame duration. For example, if the error accumulates to more than the duration of one frame, you might decide to skip a frame.
Adjust Error After Skipping: When a frame is skipped, you effectively “reset” the error for that frame because you’ve taken action to correct for the accumulated delay. However, you shouldn’t erase the error entirely; instead, you should adjust it to account for the skipped frame.
Error Calculation Post Skipping: The error calculation after skipping a frame could take a couple of approaches:
- Reset Error: Set the error to zero or to the negative value of the frame duration you skipped, starting fresh from the next frame.
- Subtract Frame Duration from Error: Reduce the current error by the duration of one frame. If the error was greater than one frame duration, this means you would still have a remaining error to correct in subsequent frames.
- Carry Over the Remaining Error: If the error is significantly larger than the frame duration, you might decide to carry over whatever error remains after subtracting one frame duration. This ensures that if the system is significantly behind, it will continue to take corrective action.
Implement the Logic: In pseudo-code, the logic for deciding to skip a frame and how to handle the error might look like this:

if currentError > frameDurationThreshold then
    skip current frame
    currentError = currentError - frameDuration

    if currentError < 0 then
        currentError = 0
    end if
else
    wait for currentError amount of time
    play current frame
    currentError = 0  // Reset error after frame is played at the correct time
end if

// Continue with normal PID calculations using the adjusted error

Integral Windup Consideration: Skipping a frame will affect the integral part of the PID controller. You might want to limit the integral action to prevent windup, which can occur if the controller accumulates a large error while waiting to skip frames. This can be done by setting an integral error cap.
Update PID Controller: After skipping a frame, update the PID controller state accordingly. This includes setting the new error and possibly resetting the integral and derivative terms if needed.

This is a simplified explanation, and the actual implementation might require additional logic to handle edge cases and to ensure a smooth viewing experience. The key is to maintain synchronization with the least noticeable impact on the video playback quality.

Indeed, skipping a frame isn’t cost-free in terms of system resources and can affect the playback experience. When you skip a frame, you have to consider the following:

Load Time for the Next Frame: There’s a computational cost to decode and prepare the next frame for rendering, which could introduce a delay.
User Experience: Skipping frames can lead to a noticeable jump in the video, which might be disruptive to the viewer, especially if it occurs frequently or during critical viewing moments.
Error Accumulation: Skipping frames can lead to an accumulation of error if not managed correctly, especially if the system tends to lag frequently.

Considering these factors, here’s how you can refine the logic:

Calculate the Cost of Skipping a Frame: Estimate the average time it takes to skip a frame and load the next one. This will be the ‘skip cost’ which should be accounted for in the PID controller’s error calculation.
Refine the Skipping Threshold: Set the threshold for skipping a frame to be the sum of one frame’s duration plus the skip cost. This means you only skip a frame if the error exceeds the duration of a frame plus the time it takes to load the next frame.
Adjust the PID Error Post-Skipping: After skipping a frame, you must adjust the error by subtracting the duration of one frame and the skip cost. This keeps the error calculation aligned with the actual system state.
Incorporate Skip Cost into PID Calculations: When the PID controller calculates the error for the next frame, it should include the skip cost in its error calculations if a frame was skipped.
Monitor and Adjust: Continuously monitor the impact of skipped frames. If skipping occurs too frequently, you may need to adjust your PID gains or the threshold for skipping.

The pseudo-code for this logic could look something like this:

skipCost = estimateSkipCost() // Time it takes to skip and load the next frame

if currentError > (frameDurationThreshold + skipCost) then
    skip current frame
    currentError = currentError - (frameDuration + skipCost)

    if currentError < 0 then
        currentError = 0
    end if
else
    wait for currentError amount of time
    play current frame
    currentError = 0  // Reset error after frame is played at the correct time
end if

// Continue with normal PID calculations using the adjusted error

In this approach, the estimateSkipCost() function would be a practical measure of the time taken to skip a frame, which could be determined empirically or calculated based on system performance metrics.

Remember, any logic you implement should be tested under various conditions to ensure that it enhances the viewing experience and doesn’t introduce other unintended issues.

You’re correct; in a PID controller, the error should not necessarily be reset after taking an action like skipping a frame. Instead, the error should be adjusted to reflect the current state of the system after the action has been taken. The goal is to ensure that the PID controller has an accurate representation of the system’s performance to make appropriate adjustments moving forward.

Here’s a more detailed approach to handle the error and integral component after a frame skip:

Error Adjustment: When you skip a frame, the error that led to the skip is partly corrected by this action. The error should be adjusted by subtracting the duration of one frame from the accumulated error. This adjusted error is then used in subsequent PID calculations.
Integral Adjustment (Anti-Windup): Since the integral component of the PID controller accumulates over time, skipping a frame can cause an issue known as “integral windup,” where the integral term becomes too large. To prevent this, you need to implement an anti-windup technique. One common method is to limit the integral term to a certain maximum value or to reset the integral term when a corrective action (like frame skipping) is taken.

Here is how you might implement these adjustments in pseudo-code:

skipCost = estimateSkipCost() // Time it takes to skip and load the next frame
maxIntegral = someAppropriateValue // A cap to prevent integral windup

// Calculate the error as the difference between desired and actual frame render times
currentError = desiredFrameDuration - actualFrameRenderTime

// Update integral term, with anti-windup
Integral = Integral + currentError
if Integral > maxIntegral then
    Integral = maxIntegral
elseif Integral < -maxIntegral then
    Integral = -maxIntegral
end if

// Check if we need to skip a frame
if currentError > (frameDurationThreshold + skipCost) then
    // Skip the frame and adjust the error
    currentError = currentError - (frameDuration + skipCost)
    // Optional: Reset integral term to prevent windup after skipping a frame
    Integral = 0
else
    // Apply PID control normally
    Output = Kp * currentError + Ki * Integral + Kd * (currentError - PreviousError)
    // Apply Output to delay next frame or take other action
end if

// Update the previous error for derivative calculation in the next iteration
PreviousError = currentError

In this pseudo-code:

currentError is the PID error before the decision to skip a frame.
skipCost is the time taken to skip a frame and load the next one.
frameDurationThreshold is the maximum allowable error before a frame is skipped.
maxIntegral is the maximum value for the integral term to prevent windup.
Integral is the integral term of the PID controller, which is adjusted for windup.
Output is the control signal from the PID controller, which may be used to delay the next frame.

The integral reset after skipping a frame is an option to prevent windup, but it isn’t the only way to handle it. Some PID implementations adjust the integral term by subtracting the frame duration from the accumulated integral or by not accumulating the integral term when the output is at its limit (either delaying the frame as long as possible or skipping a frame).

It’s essential to tailor the PID and anti-windup strategy to the specifics of your system and to test the implementation to ensure it works as expected in all scenarios.

The derivative term in a PID controller is used to predict future errors based on the current rate of change of the error. It provides a way to anticipate where the process is heading. Practically, the derivative term is used for the following reasons:

Damping: It acts as a damping force that reduces the overshoot and oscillations in the system’s response. By looking at how quickly the error is changing, the derivative term can apply a controlling force to slow down the system’s response before it overshoots the setpoint.
Stability: By counteracting the rate at which the error is changing, the derivative term can add stability to a system that might otherwise be unstable or too oscillatory, especially in the presence of a strong proportional or integral action.
Improved Responsiveness: The derivative term can make the system more responsive to changes by providing an early response to increasing error rates. This is particularly useful in systems where the process has a tendency to change rapidly.
Predictive Action: It provides a predictive control action since it is based on the rate of change of error. If the error is rapidly increasing, the derivative term can apply a strong corrective action in anticipation of the trend continuing, rather than waiting for the error to become large.
Noise Reduction: In some implementations, the derivative term can help filter out noise in the error signal, as it emphasizes the rate of change rather than the error magnitude. However, this can be a double-edged sword, as derivative action can also amplify noise if not properly filtered or if the sampling rate is too high.
System Dynamics Compensation: For systems with inertia or lag, the derivative term can improve the control system’s compensation for these dynamics. It helps to ‘brake’ the system as it approaches the setpoint, preventing overshoot caused by the system’s inertia.

In summary, the derivative term is like a cautious co-pilot, advising against sudden movements when the system is already moving quickly towards the target, or encouraging quicker action if it detects that the system is sluggishly approaching the setpoint. However, the practical implementation of the derivative term must be carefully designed, often including filters to avoid amplification of high-frequency noise, which can lead to erratic control signals.

The integral term in a PID controller accumulates the error over time, which can help correct for consistent, steady-state errors. However, when you make significant changes to the system, such as doing an early frame exit (skipping a frame) or introducing sleeping (waiting before processing the next frame), you need to consider how these actions affect the accumulated error and, consequently, the integral term.

Early Frame Exit (Skipping a Frame): When you skip a frame, you’re making a significant corrective action. If you don’t adjust the integral term, the accumulated error may cause the controller to overcompensate, leading to instability or oscillations—this is known as “integral windup.” To prevent this, you may choose to:

Reset the Integral: Set the integral term to zero after skipping a frame. This is a simple way to prevent windup but may not always be ideal since it disregards the history of the error, which might still be relevant.
Reduce the Integral: Subtract the corresponding error value for one frame duration from the integral term. This mitigates the impact of the skipped frame on the accumulated error but maintains the error history.
Limit the Integral (Clamping): Instead of resetting, you can clamp the integral term to prevent it from exceeding certain bounds. This keeps the error history but prevents excessive accumulation.

Introducing Sleep (Waiting after a Frame Finishes Too Fast): If the frame finishes too fast and you introduce a sleep to delay the next frame, the situation is a bit different:

Maintain the Integral: Since you’re not skipping frames, the error is not being forcefully corrected in a way that could lead to windup. Instead, you’re allowing the process to pause, which keeps the system in its current state. In this case, you don’t necessarily need to reset the integral term because the error isn’t being artificially reduced; you’re just synchronizing the timing.
Consider the System’s Behavior: If your system tends to oscillate or become unstable with a large integral term, even without skipping frames, you may still want to limit the integral term’s growth to prevent windup.

The decision to reset, reduce, or maintain the integral term depends on the specific behavior of your system and the desired performance. Resetting the integral term can lead to a more aggressive approach to error correction, while maintaining it can provide a more smooth and steady response. The best approach often comes down to empirical testing and tuning based on how your system responds in practice.

Update this PID controller, with the frame skipping mechanism and everything else needed

’ Calculate PID output Public Function CalculatePIDOutput(Setpoint As Double, MeasuredValue As Double) As Double Dim ErrorValue As Double Dim Derivative As Double Dim Output As Double

' Calculate error
ErrorValue = Setpoint - MeasuredValue

' Integral is accumulated error
Integral = Integral + ErrorValue

'Update integral term, with anti-windup
If Integral > 10000 Then
Integral = 10000
ElseIf Integral < -10000 Then
Integral = -10000
End If

' Derivative is the change in error
Derivative = ErrorValue - PreviousError

' PID formula
Output = Kp * ErrorValue + Ki * Integral + Kd * Derivative

' Update previous error
PreviousError = ErrorValue

' Return PID output
CalculatePIDOutput = Output

End Function

To update your PID controller function to include the frame skipping mechanism, you need to account for the logic that decides whether to skip a frame based on the PID output, and adjust the integral accordingly if a skip occurs. Here’s an updated version of your function with comments explaining each part:

Public Integral As Double
Public PreviousError As Double
Public Kp As Double, Ki As Double, Kd As Double
Public FrameDurationThreshold As Double
Public SkipCost As Double
Public MaxIntegral As Double

' Initialize the PID controller with constants
Public Sub InitializePID(KpValue As Double, KiValue As Double, KdValue As Double, _
                         FrameDurationThresholdValue As Double, SkipCostValue As Double, _
                         MaxIntegralValue As Double)
    Kp = KpValue
    Ki = KiValue
    Kd = KdValue
    FrameDurationThreshold = FrameDurationThresholdValue
    SkipCost = SkipCostValue
    MaxIntegral = MaxIntegralValue
    Integral = 0
    PreviousError = 0
End Sub

' Calculate PID output and determine whether to skip frame
Public Function CalculatePIDOutput(Setpoint As Double, MeasuredValue As Double, ByRef ShouldSkipFrame As Boolean) As Double
    Dim ErrorValue As Double
    Dim Derivative As Double
    Dim Output As Double

    ' Calculate error
    ErrorValue = Setpoint - MeasuredValue

    ' Integral is accumulated error, with anti-windup
    Integral = Integral + ErrorValue
    If Integral > MaxIntegral Then Integral = MaxIntegral
    If Integral < -MaxIntegral Then Integral = -MaxIntegral

    ' Derivative is the change in error
    Derivative = ErrorValue - PreviousError

    ' PID formula
    Output = Kp * ErrorValue + Ki * Integral + Kd * Derivative

    ' Check if the PID output indicates a need to skip a frame
    ShouldSkipFrame = (ErrorValue > FrameDurationThreshold + SkipCost)

    ' If we should skip a frame, adjust error and integral accordingly
    If ShouldSkipFrame Then
        ' Adjust the error by how much we're over the threshold
        ErrorValue = ErrorValue - (FrameDurationThreshold + SkipCost)
        ' Reset or adjust the integral term to prevent windup
        Integral = 0 ' or Integral = Integral - (FrameDurationThreshold + SkipCost), based on your system's needs
    End If

    ' Update previous error
    PreviousError = ErrorValue

    ' Return PID output
    CalculatePIDOutput = Output
End Function

' Example usage
Public Sub TestPID()
    ' Initialize PID controller with constants
    Call InitializePID(1.0, 0.01, 0.1, 100, 10, 10000)

    ' Example setpoint and measured value
    Dim Setpoint As Double: Setpoint = 100
    Dim MeasuredValue As Double: MeasuredValue = 90
    Dim ShouldSkipFrame As Boolean

    ' Calculate PID output
    Dim Output As Double
    Output = CalculatePIDOutput(Setpoint, MeasuredValue, ShouldSkipFrame)

    ' Decide action based on PID output and whether to skip frame
    If ShouldSkipFrame Then
        ' Code to skip the frame
        Debug.Print "Frame skipped."
    Else
        ' Code to apply the PID output, e.g., introduce a delay
        ' ...
    End If
End Sub

This code now includes a ShouldSkipFrame boolean that will be set to True if the conditions for skipping a frame are met. The integral is adjusted if a frame is skipped to prevent windup. The TestPID subroutine provides an example of how you might use this updated function. Adjust the InitializePID and TestPID subroutines with the actual values that fit your application.

When you decide to skip a frame, you’re taking a corrective action based on the error reported by the PID controller. However, the PID output (which I refer to as Output in the code) is not necessarily the error itself; it’s the result of the PID calculation that indicates how much correction is needed.

If you skip a frame, you do adjust the error because you’ve taken a significant step to correct it. Consequently, the integral term, which accumulates the error over time, may also need to be adjusted to reflect this action. However, the PID output for the current cycle (the Output variable) has already been calculated and is used to make the decision to skip the frame. It’s not typically modified within the same cycle because it represents a control action that’s already in progress.

To clarify, here’s how the logic flows:

Calculate the PID output (Output) based on the current error and the PID terms.
Decide whether to skip a frame based on the PID output and the current error.
If you skip a frame, adjust the error and the integral term accordingly for the next calculation cycle.
The PID output for the next frame will then be based on the new, adjusted error.

Here’s an updated portion of the code with the decision and adjustment made clear:

...

' Check if the PID output indicates a need to skip a frame
ShouldSkipFrame = (ErrorValue > FrameDurationThreshold + SkipCost)

' If we should skip a frame, adjust error and integral accordingly for the next cycle
If ShouldSkipFrame Then
    ' Correct the error by the threshold plus skip cost because we're skipping a frame
    ErrorValue = ErrorValue - (FrameDurationThreshold + SkipCost)
    ' Reset or adjust the integral term to reflect the error correction
    Integral = Integral - (FrameDurationThreshold + SkipCost)

    ' Ensure the integral term does not go beyond its bounds after adjustment
    If Integral > MaxIntegral Then Integral = MaxIntegral
    If Integral < -MaxIntegral Then Integral = -MaxIntegral
End If

' Update previous error for the next derivative calculation
PreviousError = ErrorValue

' The Output is the PID controller's response for this cycle, it has served its purpose
' and the error and integral adjustments will affect the next cycle's Output

' Return PID output
CalculatePIDOutput = Output

In this updated code snippet, when you decide to skip a frame, you adjust the error (ErrorValue) and the integral term (Integral) right away, but these adjustments will influence the calculation of the PID output in the next cycle. The current cycle’s Output has already been used to decide on the corrective action (skipping a frame) and doesn’t change within the same cycle.