====== What is PID control ======
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**PID Control**
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\\ - 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 ∫e(𝜏)d𝜏} + {Kd x de(t)/dt}
\\ - u(t): control signal
\\ - e(t) = Set point - process variable
\\ - Kp: Proportional gain, Ki: Integral gain, Kd: Derivative gain
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**(i) Proportional**
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\\ - The error is corrected in proportion to its current magnitude.
\\ - P control output = Kp x Error
\\ - If Kp is too large, overshoot and oscillation may occur.
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**(ii) Integral**
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\\ - 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 ∫(Error)dt
\\ - If Ki is too large, the system may respond slowly or become unstable.
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**(iii) Derivative**
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\\ - 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.