Me can try Vp+ Vps( Pd controller )or i2( Lead or Lag Ds term has the problem of amplifying noise and O Next, consider the canonical system 32+Ii+= for relative stability spec- nn ification and try to design a controller d) that satisfy the following system In this case. overshoot <5 ≤ (5%)settling time <2(sec) g Here. the roots of the above canonical system is and the above requirements are mapped as follows in the complex plane In other words, the closed loop poles must be in the shaded region absolute stabilit The shaded region where the closed loop poles must be Now, as an example, consider the plant s(s+'s motor system )and apply✚ ￾❬➂❑③❣■❢⑨❍❡❜❯P✂✁✗✙✔ ✁☎✄ ✶ ❵✒❱✘❴ ❑✎❋✪❢❦❍❡❜❝❋✪❲❚❲❚❬✎❜❆♣✻❋✪❜ ✢✝✆✟✞ ✢✝✆✡✠ ❵✒❏✷❬③❣■❩➍❋✪❜❊❏✂❣■❧❀♣⑩❈ ✚ ✑✄ ✶✗❍❡❬✎❜❝②➐t✾❣■▼✌❍❡t✵❬➂❞✵❜❝❋✪➇✵❲❚❬✎② ❋✿✝❣■②✏❞✵❲❚❙✆✿P●❙❚❢✵❧➅❢✵❋✪❙❚▼❝❬➂❣■❢✵❩ ✑✄ ✢ ✢✝✆✡✠ ❙❚▼ ❍❡t✵❬➂➇❃❬⑦❍❝❍❡❬✎❜❊❑✉t✵❋✪❙❚❑✎❬■❈ ☛ ❖❆❬✤✣●❍③➋✳❑✎❋✪❢✵▼❝❙❚❩✵❬✎❜✘❍❡t✵❬➃❑③❣■❢✵❋✪❢✵❙❚❑③❣■❲❽▼❯P●▼❯❍❡❬✎② ☞✍✌✎ ✢ ✌ ✆✡✏✒✑☞✎ ✢✝✆☞✎✌ ✿❋✪❜❹❜❝❬✎❲④❣♦❍❡❙♥♠✪❬❊▼❯❍✉❣■➇✵❙❚❲❚❙♥❍❥P❿▼❝❞❃❬✎❑⑩❤ ❙✆☎✾❑③❣♦❍❡❙❚❋✪❢❀❣■❢✵❩✏❍❡❜❯P❛❍❡❋➅❩✵❬✎▼❝❙❚❧✪❢☎❣❭❑✎❋✪❢❦❍❡❜❝❋✪❲❚❲❚❬✎❜✔✓❀❵ ✶❸♣✒❍❡t✾❣♦❍ ▼❡❣♦❍❡❙❚▼ ✿P❿❍❡t✵❬ ✿❋✪❲❚❲❚❋➉❊❙❚❢✵❧✗▼❯P●▼❯❍❡❬✎② ▼❝❞❃❬✎❑✎❙✆☎✾❑③❣♦❍❡❙❚❋✪❢✵▼✎❈ ❫❥❢✠❍❡t✵❙❚▼✌❑③❣■▼❝❬■➋❽❋♠✪❬✎❜❝▼❝t✵❋●❋■❍ ✰ ➆✳✲ ✕ ✖✓✌ ✛ ✗ ✏ ✕ ✘ ✰✚✙✛ ❵➎➆✳✲❛♣ ▼❝❬⑦❍❝❍❡❲❚❙❚❢✵❧ ❍❡❙❚②✏❬ ✰ ◆✠❵ ✶✞✷✞✸✎♣ ✕ ✖✢✜✤✣ ✌✦✥★✧ ✥ ✩✫✪ ✛ ❇ ✴ ➈❦➆ ✯❆❬✎❜❝❬■➋✾❍❡t✵❬➂❜❝❋●❋■❍❡▼✌❋✿s❍❡t✵❬❭❣■➇❃❋♠✪❬➂❑③❣■❢✵❋✪❢✵❙❚❑③❣■❲✷▼❯P●▼❯❍❡❬✎② ❙❚▼ ✶ ✛✒✬ ✏ ✛✮✭✯✖✢✜✤✣✱✰✲✜✤✣✴✳❇✱✭✲✖ ✏ ❣■❢✵❩✠❍❡t✵❬❭❣■➇❃❋♠✪❬➂❜❝❬✎◗❘▲✵❙❚❜❝❬✎②✏❬✎❢❦❍❡▼➃❣■❜❝❬✗②❀❣■❞✵❞❃❬✎❩⑧❣■▼✄✿❋✪❲❚❲❚❋➉❊▼✌❙❚❢⑨❍❡t✵❬➂❑✎❋✪②✏❞✵❲❚❬✤✣⑨❞✵❲④❣■❢✵❬■❈ ❫❥❢➍❋■❍❡t✵❬✎❜✌➉✻❋✪❜❝❩✵▼✎➋✾❍❡t✵❬➂❑✎❲❚❋✪▼❝❬✎❩✠❲❚❋●❋✪❞✠❞❃❋✪❲❚❬✎▼✌②▲✵▼❯❍❊➇❃❬➂❙❚❢⑨❍❡t✵❬➂▼❝t✾❣■❩✵❬✎❩⑧❜❝❬✎❧✪❙❚❋✪❢ ❈ overshoot requirements absolute stability boundary settling time requirements Im s Re s r✌t✵❬➂▼❝t✾❣■❩✵❬✎❩⑧❜❝❬✎❧✪❙❚❋✪❢⑨➉❊t✵❬✎❜❝❬➂❍❡t✵❬➂❑✎❲❚❋✪▼❝❬✎❩✠❲❚❋●❋✪❞⑨❞❃❋✪❲❚❬✎▼❊②▲✵▼❯❍❊➇❃❬■❈ ❖❆❋➉➂➋✒❣■▼➅❣■❢ ❬✤✣✵❣■②✏❞✵❲❚❬■➋s❑✎❋✪❢✵▼❝❙❚❩✵❬✎❜➂❍❡t✵❬❀❞✵❲④❣■❢❦❍ ✛ ✢✒✵ ✢✝✆ ✛✝✶ ❵✌②✏❋■❍❡❋✪❜✗▼❯P●▼❯❍❡❬✎② ♣➂❣■❢✵❩ ❣■❞✵❞✵❲♥P ❪