Lead Compensator Second Order Type 1, Step Response and Root Locus

Cuthbert Nyack
The applets below show the effect of sampling on the step response and root locus of a type 1 second order system with Lead Compensation.
With parameters (20.0, 0.5, 0.28, 0.1, 0.01, 0.1, 1.0), there is close correspondence between the step response of the continuous and sampled system. The closed loop poles are at -0.9573, 0.8513 ± j 0.0775
With parameters (20.0, 0.5, 0.28, 0.1, 0.19, 1.0, 1.0), the complex conjugate poles have moved outside the unit circle and the system is unstable. With Ts =0.18, the poles are close to the unit circle and there is a sharp peak in the closed loop frequency response at ~ 0.34ws. This frequency can also be determined from (180 - atan(0.8290/0.549))/360 = 0.3431ws.

Applet below show an expanded view of the one above.

Gif images below show how the applets should appear.

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COPYRIGHT 2006 Cuthbert Nyack.