Switching Line

Id OPTIMAL DAMPING

Fig. 19-12. State Plane Trajectories for a Bang-Bang Control System

Id OPTIMAL DAMPING

Fig. 19-12. State Plane Trajectories for a Bang-Bang Control System brief time after the switching line is crossed. This approach reduces actuator wear but may lead to instabilities.

Optimal Damping. We would like to design a system which will approach the origin in an efficient manner for any initial condition. From Fig. 19- 12(b) it is apparent that the origin can be approached from only two directions, labeled Q and Q'. Thus, we would prefer to use as switching lines those parabolas which pass through the origin. This is algebraically described by u= — U sign

U0+j

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