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--- what_is_pid_control [2025/05/12 12:59] – arim
+++ what_is_pid_control [2025/05/12 15:29] (current) – arim
@@ Line 8: / Line 8: @@
 \\ - A feedback-based control loop that compares the actual value with the target value.
 \\ - Combining the Proportional, Integral, and Derivative components, PID control reduces the system's error to make the output reach the set point and maintain that sate effectively.
-\\ - u(t) = {Kp x e(t)} + {Ki x Ie(r)dr} + {Kd x de(t)/dt}
+\\ - u(t) = {Kp x e(t)} + {Ki x ∫e(𝜏)d𝜏} + {Kd x de(t)/dt}
 \\ - u(t): control signal
 \\ - e(t) = Set point - process variable
@@ Line 15: / Line 15: @@
 \\
 **(i) Proportional**
-\\ <color #00a2e8>(photo): Waveform comparison: (Small Kp) vs (Large Kp)</color>
+\\ {{ :p_control.jpg?direct&400 |}}
 \\ - The error is corrected in proportion to its current magnitude.
 \\ - P control output = Kp x Error
@@ Line 22: / Line 22: @@
 \\
 **(ii) Integral**
-\\ <color #00a2e8>- Waveform comparison: (Kp + Kd) vs (Kp + Kd + Ki)
+\\ {{ :i_control.jpg?direct&400 |}}
-</color>\\ - The error is corrected by considering the accumulated error over time.
+\\ - The error is corrected by considering the accumulated error over time.
 \\ - It helps eliminate small, long-standing errors, known as steady-state error.
-\\ - I control output = Ki x I(Error)dt
+\\ - I control output = Ki x ∫(Error)dt
 \\ - If Ki is too large, the system may respond slowly or become unstable.
 \\
 \\
 **(iii) Derivative**
-\\ -<color #00a2e8> Waveform comparison: (Kp only) vs (Kp + Kd)</color>
+\\ {{ :d_control.jpg?direct&400 |}}
 \\ - The derivative term predicts future error by analyzing the rate of change of the error and suppresses excessive responses.
 \\ - D control output = Kd x d(Error)/dt
 \\ - It reduces oscillation and helps stabilize the system smoothly.