c# - PID Controller 积分项导致极度不稳定

Question

我有一个在机器人上运行的 PID Controller ，旨在使机器人转向罗盘航向。 PID 校正以 20Hz 的速率重新计算/应用。

尽管 PID Controller 在 PD 模式(即，积分项归零)下运行良好，但即使是最少量的积分也会迫使输出不稳定，从而导致转向执行器被推向左侧或左侧右极端。

代码:

        private static void DoPID(object o)
    {
        // Bring the LED up to signify frame start
        BoardLED.Write(true);

        // Get IMU heading
        float currentHeading = (float)RazorIMU.Yaw;

        // We just got the IMU heading, so we need to calculate the time from the last correction to the heading read
        // *immediately*. The units don't so much matter, but we are converting Ticks to milliseconds
        int deltaTime = (int)((LastCorrectionTime - DateTime.Now.Ticks) / 10000);

        // Calculate error
        // (let's just assume CurrentHeading really is the current GPS heading, OK?)
        float error = (TargetHeading - currentHeading);

        LCD.Lines[0].Text = "Heading: "+ currentHeading.ToString("F2");

        // We calculated the error, but we need to make sure the error is set so that we will be correcting in the 
        // direction of least work. For example, if we are flying a heading of 2 degrees and the error is a few degrees
        // to the left of that ( IE, somewhere around 360) there will be a large error and the rover will try to turn all
        // the way around to correct, when it could just turn to the right a few degrees.
        // In short, we are adjusting for the fact that a compass heading wraps around in a circle instead of continuing
        // infinity on a line
        if (error < -180)
            error = error + 360;
        else if (error > 180)
            error = error - 360;

        // Add the error calculated in this frame to the running total
        SteadyError = SteadyError + (error * deltaTime);

        // We need to allow for a certain amount of tolerance.
        // If the abs(error) is less than the set amount, we will
        // set error to 0, effectively telling the equation that the
        // rover is perfectly on course.
        if (MyAbs(error) < AllowError)
            error = 0;

        LCD.Lines[2].Text = "Error:   " + error.ToString("F2");

        // Calculate proportional term
        float proportional = Kp * error;

        // Calculate integral term
        float integral = Ki * (SteadyError * deltaTime);

        // Calculate derivative term
        float derivative = Kd * ((error - PrevError) / deltaTime);

        // Add them all together to get the correction delta
        // Set the steering servo to the correction
        Steering.Degree = 90 + proportional + integral + derivative;

        // We have applied the correction, so we need to *immediately* record the 
        // absolute time for generation of deltaTime in the next frame
        LastCorrectionTime = DateTime.Now.Ticks;

        // At this point, the current PID frame is finished
        // ------------------------------------------------------------
        // Now, we need to setup for the next PID frame and close out

        // The "current" error is now the previous error
        // (Remember, we are done with the current frame, so in
        // relative terms, the previous frame IS the "current" frame)
        PrevError = error;

        // Done
        BoardLED.Write(false);
    }

有没有人知道为什么会发生这种情况或如何解决？

Answer 1

看起来您正在将时基应用于积分 3 次。 错误已经是自上次样本以来的累积错误，因此您不需要将 deltaTime 乘以它。所以我将代码更改为以下内容。

SteadyError += 错误;

SteadyError 是误差的积分或总和。

所以积分应该只是 SteadyError * Ki

浮点积分 = Ki * SteadyError;

编辑:

我已经再次检查了您的代码，除了上述修复之外，还有其他几个项目需要修复。

1) 您不需要以毫秒为单位的增量时间。在正常的采样系统中，delta 项将为 1，但您为 20Hz 的速率输入了一个类似 50 的值，这具有将 Ki 增加该系数并同时将 Kd 减小 50 倍的效果。如果您担心抖动，则需要将增量时间转换为相对采样时间。我会改用公式。

float deltaTime = (LastCorrectionTime - DateTime.Now.Ticks)/500000.0

500000.0 是每个样本的预期滴答数，对于 20Hz 是 50ms。

2) 将积分项保持在一个范围内。

if ( SteadyError > MaxSteadyError ) SteadyError = MaxSteadyError;
if ( SteadyError < MinSteadyError ) SteadyError = MinSteadyError;

3) 更改以下代码，以便当误差在 -180 左右时，您不会因小的更改而出错。

if (error < -270) error += 360;
if (error >  270) error -= 360;

4) 验证 Steering.Degree 是否收到正确的分辨率和标志。

5) 最后，您可能只需将 deltaTime 一起删除并按以下方式计算微分项。

float derivative = Kd * (error - PrevError);

有了所有这些，您的代码就变成了。

private static void DoPID(object o)
{
    // Bring the LED up to signify frame start
    BoardLED.Write(true);

    // Get IMU heading
    float currentHeading = (float)RazorIMU.Yaw;


    // Calculate error
    // (let's just assume CurrentHeading really is the current GPS heading, OK?)
    float error = (TargetHeading - currentHeading);

    LCD.Lines[0].Text = "Heading: "+ currentHeading.ToString("F2");

    // We calculated the error, but we need to make sure the error is set 
    // so that we will be correcting in the 
    // direction of least work. For example, if we are flying a heading 
    // of 2 degrees and the error is a few degrees
    // to the left of that ( IE, somewhere around 360) there will be a 
    // large error and the rover will try to turn all
    // the way around to correct, when it could just turn to the right 
    // a few degrees.
    // In short, we are adjusting for the fact that a compass heading wraps 
    // around in a circle instead of continuing infinity on a line
    if (error < -270) error += 360;
    if (error >  270) error -= 360;

    // Add the error calculated in this frame to the running total
    SteadyError += error;

    if ( SteadyError > MaxSteadyError ) SteadyError = MaxSteadyError;
    if ( SteadyError < MinSteadyError ) SteadyError = MinSteadyError;

    LCD.Lines[2].Text = "Error:   " + error.ToString("F2");

    // Calculate proportional term
    float proportional = Kp * error;

    // Calculate integral term
    float integral = Ki * SteadyError ;

    // Calculate derivative term
    float derivative = Kd * (error - PrevError) ;

    // Add them all together to get the correction delta
    // Set the steering servo to the correction
    Steering.Degree = 90 + proportional + integral + derivative;

    // At this point, the current PID frame is finished
    // ------------------------------------------------------------
    // Now, we need to setup for the next PID frame and close out

    // The "current" error is now the previous error
    // (Remember, we are done with the current frame, so in
    // relative terms, the previous frame IS the "current" frame)
    PrevError = error;

    // Done
    BoardLED.Write(false);
}