1. A unity feedback control system has an open-loop transfer function given by Eq. (1), Design in detail a lag compensator so that the phase margin of the compensated system is 40o and the steady state error to ramp input is less than or equal to 0.2. Verify your design in MATLAB by obtaining the phase margin of the compensated system using Bode command.
G(s) = k/s(s+ 2s)
2. A type 2 unity feedback system has an open-loop transfer function given by Eq.2. Use MATLAB to design a lead compensator to meet the following specifications:
- Settling time < 2 seconds.
- Peak overshoot to step input < 25%
G(s)H(s) = k/s2(s+1.5)