Topic: Control Systems
The standard form of a PID controller is
- A. $K_{p}+K_{d}s+K_{I}s^{2}$
- B. $K_{p}+\frac{K_{d}}{s}+\frac{K_{I}}{s^{2}}$
- C. $K_{p}+K_{d}\cdot s+\frac{K_{I}}{s}$
- D. $K_{p}\cdot s+K_{d}s^{2}+K_{I}s$
Answer: C. $K_{p}+K_{d}\cdot s+\frac{K_{I}}{s}$
Explanation: A PID (Proportional-Integral-Derivative) controller produces an output signal consisting of three terms: a proportional term ($K_p$), an integral term which is divided by $s$ in the Laplace domain ($\frac{K_I}{s}$), and a derivative term which is multiplied by $s$ in the Laplace domain ($K_d s$). Thus, the transfer function is $C(s) = K_p + K_d s + \frac{K_I}{s}$.