Design Project 1 for EE4580As in the distributed notes, the linearized model for inverted pendulum consists of twotransfer functions. We aim to designGyu(s)andGθu(s) such that the dominant dynamics forthe closed-loop system have damping ratio 0.83, and natural frequency 1.83. Moreover thesteady-state error for the position of the cart is zero. The design can proceed as follows:1. We consider ﬁrst design ofG(s)=num(s)deng(s)=Kgys+zys+pgGθu(snumθu(s)deng(s)=Kgθs+zθs+pgsuch that the transient performance is satisﬁed. Iterative design method can be employedusing both 0oand 180oroot locus methods.2. We then modify the compensators into the formG(snum(s)deng(s)=K(s+zy)(s+z²)s(s+pg)Gθu(snumθu(s)deng(s)=Ks+zθs+pgwithz²>0 a very small number. Note that other parameters need be adjusted approri-ately in order to satisfy the transient performance reqirements.
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