Engineering domain: Control Design

## Task Description
You need to design a PID controller for a magnetic levitation system in which an electromagnet holds a steel ball at a desired height. Near the operating point, the nonlinear dynamics can be linearized and modeled by the transfer function:
G = K / ((tau1*s + 1)*(tau2*s + 1)*(tau3*s + 1));
where:
K  = 1;
tau1 = 0.5;
tau2 = 1.0;
tau3 = 2.0;

Design a PID controller so that the closed‑loop system meets all of the following specifications:
1. Settling time Ts (to within plus or minus 5 percent) < 5s
2. Overshoot < 20 percent
3. Zero steady state error to a unit step input
4. Gain margin > 10dB
5. Phase margin > 45 degrees

## Output format
You need to give me your Kp, Ki, and Kd in numerical form.