Fall 2001 16.3115-2 Could also choose the closed-loop poles to mimic a system that has similar performance to what you would like to achieve Just set pole locations equal to those of the prototype system Various options exist Bessel Polynomial Systems of order k -Gp(s)=Bs Step response of Gp for various k k=1 0.6 04 0.2 1.0 3.0 Time(seconds) Roots of normalized Bessel polynomials corresponding to a settling time of one second of Bk (s) 4.6200 24.0530±/23400 3-50093,39668±37845 4-4.0156±50723.55281±j6553 546448041104±63142.59268/30813 642169±尸530062613±44018,7.1205±14540 -80271,4.361±A8.7519,6.5714±.6786,-7.6824±28081 844554±9715,6855+1692788.1682±A41057,8.7693±3616 99658545696±/11871145815.85962±/5365594013±2665 104683512403373609±377,898:6057,49657±9342.104278±13071 All scaled to give settling times of 1 second, which ou can change to ts by dividing the poles by tsFall 2001 16.31 15—2 • Could also choose the closed-loop poles to mimic a system that has similar performance to what you would like to achieve: — Just set pole locations equal to those of the prototype system. — Various options exist • Bessel Polynomial Systems of order k → Gp(s) = 1 Bk(s) • All scaled to give settling times of 1 second, which you can change to ts by dividing the poles by ts