A proportional-integral-derivative $\text{(PID)}$ controller is employed to stably control a plant with transfer function
$$P(s) = \frac{1}{(s+1)(s+2)}$$
Now, the proportional gain is increased by a factor of $2,$ the integral gain is increased by a factor of $3,$ and the derivative gain is left unchanged. Given that the closed-loop system continues to remain stable with the new gains, the steady-state error in tracking a ramp reference signal _________
- Remains unchanged
- Decreases by a factor of $2$
- Decreases by a factor of $3$
- Decreases by a factor of $5$