Design a Lag controller using root locus techniques for the plant,
such that the following performance specifications are met:
What will be an ideal response?
Step 1:
Pick the lag zero (-A) to lie at 
distance of the nearest pole or zero to the origin. The plant has no zeros and poles at 
The nearest pole, neglecting the pole at the origin, is about 10 units from the origin (it is actually located at 
so the lag zero is chosen as:
Step 2: Because the system is type 1 the steady state step error spec is satisfied by default.
To design the ramp error to spec, select: 
is easily computed by evaluating the plant transfer function at s = 0 to produce 
is computed from the 
specification. Note that we are designing to the boundary, or worst case, of this specification. The calculation is presented below.
Step 3:
Select the lag pole 
Step 4:
The lag compensator transfer function is,
This compensator is implemented in the cascade configuration shown in the following figure.
The control system is stable and the unit ramp response and associated error signal is shown below.
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