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A discrete PID controller is used to set the speed of a motor. The set point for the motor, as measured by the speed sensor is 5V. The table below shows the actual output values for each loop of the controller program. The table: In the left hand column - Time (ms): 0, 49.9, 99.8, 149.7. In the right hand column - Speed (V): 0, 0.85, 2.9, 4.05. If the controller has settings of Kp = 2.59, Ki = 0.00208, Kd = 6 (with all units defined in time units of ms), what is the current output value of the PID controller in V?



Answer = 3.28V. Please show each step with numerical working and check that the value you obtain is actually 3.28V. I am yet to see anyone get this correct. Thank you.

A discrete PID controller is used to set the speed of a motor The set point for the motor as measured by the speed sensor

Answer :

The current output value of the PID controller is approximately 6.59 V.

Calculate the current output value of the PID controller, combining the provided information and following the steps for a discrete PID controller:

1. Gather necessary data:

Set point (SP) = 5V

Actual speed values: [0, 0.85, 2.9, 4.05] V

Time intervals: [49.9, 49.9, 49.9] ms

PID gains: Kp = 2.59, Ki = 0.00208, Kd = 6

2. Calculate errors for each time interval:

Error at time 49.9 ms = SP - Actual speed = 5 - 0 = 5 V

Error at time 99.8 ms = 5 - 0.85 = 4.15 V

Error at time 149.7 ms = 5 - 2.9 = 2.1 V

3. Calculate proportional component (P):

P = Kp * Current Error = 2.59 * 2.1 = 5.439 V

4. Calculate integral component (I):

Sum of errors = 5 + 4.15 + 2.1 = 11.25 V*ms

I = Ki * Σ(Errors) * Δt = 0.00208 * 11.25 * 49.9 = 1.154 V

5. Calculate derivative component (D):

Change in error = (2.1 - 4.15) / 49.9 = -0.0412 V/ms

D = Kd * (Change in error) / Δt = 6 * (-0.0412) / 49.9 = -0.0050 V

6. Combine P, I, and D components:

PID output = P + I + D = 5.439 + 1.154 - 0.0050 = 6.588 V

Therefore, the current output value of the PID controller is approximately 6.59 V.

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