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Ex. 1. Review Bode, Nyquist and Nichols charts. Plot different
transfer functions and play with it by modifing the parameters, adding delays, etc.
Ex. 2. Prove that the loci of the sensitivity function
|1/(L+1)|=constant on a Nichols chart, is "upside-down" the loci of the complementary
sensitivity, |L/(1+L)|=constant.
Ex. 3. Prove that the steady-state error coefficient e1 is equal
to 1/w1. w1 is the frequency intercepted by the asymptote at the zero dB axis
in the Bode diagram (see fig 8.1b in the first set of lecture notes).
Ex. 4. Try to improve Ljung's design example described at
the end of the the first set of lecture notes, by loopshaping
on the Nichols chart.
Ex. 5. Try to solve the problem in section 9.2 of the first set
of lecture notes (the last page).
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