H2 and H Infinity Optimization with a Restricted Region of Stability
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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Many modern control design methods, such as H2 and H Infinity optimization, guarantee that the closed-loop system will be stable. To make further use of this guarantee, the portion of the s-plane considered to be stable is restricted to a region left of a vertical line some distance alpha from the imaginary axis. This alpha shift was accomplished in the state space equations, so standard computational tools still work. now the system is not only guaranteed to be stable, but also has some guaranteed speed for the time response. The equations for guaranteeing some arbitrary damping ratio were also derived in Cartesian coordinates, but only the alpha shift was put into the state space equation form and tested. The alpha shift increased the speed of the system, as expected. An additional benefit was increasing the damping of lightly damped poles. The cost for doing this was an increase in the steady state error and an increase in the control power required.
- Operations Research