Recursive Kp Adjustment for Adaptive PID Control Error Compensation Under Timing Constraints

PID control is widely used for DC motor control in embedded systems. However fixed PID coefficients can lead to inaccurate responses under disturbances or high-frequency noise. This paper proposes an adaptive control system that dynamically adjusts PID coefficients based on real-time output analysis. When high-frequency noise is detected in the motor output signal, the system reduces the proportional gain(Kp), which narrows the bandwidth of the system transfer function. This makes the system less responsive to rapid changes, effectively filtering out the impact of high-frequency components. On the other hand, when an external disturbance causes the output to diverge from the target value, increasing Kp shifts the system poles further to the left in the s-plane. This leads to a higher damping ratio and a faster transient response, enabling the system to quickly return to the desired output with minimal overshoot. However, performing PID computation together with frequency and disturbance analysis may exceed the allowed time within a control cycle. To overcome this, the system uses the Goertzel algorithm instead of FFT for frequency detection. Unlike FFT, Goertzel incrementally processes each output sample using a recursive method, reducing run time and ensuring real-time execution.