Control sytem analysis technique

Type 1 system → zero steady-state error for step input, finite error for ramp input. The system is stable with good phase margin (≈ 55°).

This is a third-order Type 1 system, since it has three poles and one pole located at the origin. The presence of the pole at the origin means the system can track a step input with zero steady-state error, but it will have a finite error for a ramp input.

The velocity constant (Kv), which determines the steady-state error for a unit ramp input, is calculated as Kv=1K_v = 1Kv​=1. Therefore, the steady-state error (ess) for a unit ramp input is ess=1/Kv=1e_{ss} = 1 / K_v = 1ess​=1/Kv​=1.

Frequency response analysis using the Bode plot shows that the system has a gain margin of approximately 16.9 dB and a phase margin of about 55.6°, indicating that the system is stable and possesses a reasonable degree of robustness.

The closed-loop step response demonstrates that the system responds smoothly to a step input, with moderate overshoot and a stable settling behavior. Overall, the system exhibits stable performance, suitable for basic control applications but may need a compensator (like a PI or PID controller) to reduce the steady-state error for ramp inputs or to improve transient response.