Introduction to Modern Control Theory (1)Classical Control Techniques 1.Root Locus 2.Nyquist Plot 3.Bode Plot 4.PID(Proportional-Integral-Derivative )Control Technique Features 1.Limited to Linear Time Invariant Systems 2.Frequency Domain Design Technique 3.Limited to Single-Input Single-Output System (2)Modern control techniques 1.Optimal Control√ 2.Kalman Filter√ 3.Adaptive Control√ 4.Nonlinear Control√ 5.Robust Control 6.Intelligent Control√ (Neural Network,Fuzzy Control,Genetic Algorithm Features 1
✂✁☎✄✝✆✝✞✠✟☛✡☛☞✌✄✝✍✎✞✏✁✑✄✒✞✔✓✞✠✟✖✕✗✆✘✁✚✙✛✞✏✁☎✄✝✆✝✞✏✜✣✢✥✤✖✕✦✞✏✆✒✧ ★✪✩✒✫✭✬✯✮✱✰✝✲✳✲✵✴✱✶✷✰✘✮✠✬✹✸✻✺✻✼✵✽✾✸✻✮❀✿✏❁✂✶❃❂✗✺✗✴✱❄❆❅✦❁✂✲ ❇✪❈❊❉❊❋●❋■❍❆❏✷❋●❑✎▲✵▼ ◆●❈❊❖❊P●◗❘▲✵❙❚▼❯❍✦❱✝❲❚❋■❍ ❳✳❈❊❨✻❋●❩✵❬❭❱✝❲❚❋■❍ ❪ ❈❊❱✝❫✱❴❛❵✝❱✝❜❝❋✪❞❃❋✪❜❯❍❡❙❚❋✪❢✾❣■❲✐❤❥❫❥❢❦❍❡❬✎❧✪❜❡❣■❲✐❤✱❴✦❬✎❜❝❙♥♠■❣♦❍❡❙♥♠✪❬❆♣❊q✻❋✪❢❦❍❡❜❝❋✪❲✷rs❬✎❑✉t✵❢✵❙❚◗❘▲✵❬ ✈❁✂✰✇✼✾❅✦✽✾❁✂✲ ① ❇✪❈❊❏✷❙❚②✏❙♥❍❡❬✎❩☎❍❡❋✏❏✷❙❚❢✵❬③❣■❜✌r✌❙❚②✏❬✦❫❥❢❦♠■❣■❜❝❙④❣■❢❦❍✦⑤❘P●▼❯❍❡❬✎②✏▼ ◆●❈❊⑥✾❜❝❬✎◗❘▲✵❬✎❢✵❑⑦P⑧❴✦❋✪②❀❣■❙❚❢⑨❴✦❬✎▼❝❙❚❧✪❢✠rs❬✎❑✉t✵❢✵❙❚◗❘▲✵❬ ❳✳❈❊❏✷❙❚②✏❙♥❍❡❬✎❩☎❍❡❋❀⑤●❙❚❢✵❧✪❲❚❬⑩❤❥❫❥❢✵❞✵▲✳❍❆⑤●❙❚❢✵❧✪❲❚❬⑩❤❯❶✦▲✳❍❡❞✵▲✳❍❆⑤❘P●▼❯❍❡❬✎② ★❸❷❹✫✯❺❻✸❊❼✗❁✂✽❽✺❾✶✷✸✻✺✻✼✵✽✾✸✻✮❿✼✵❁✂✶❃❂✗✺✗✴✱❄❆❅✦❁✂✲ ❇✪❈❆❶✦❞✳❍❡❙❚②❀❣■❲✷q✻❋✪❢❦❍❡❜❝❋✪❲✝➀ ◆●❈❊➁➂❣■❲❚②❀❣■❢✠⑥✇❙❚❲♥❍❡❬✎❜➃➀ ❳✳❈✌➄➃❩✾❣■❞✳❍❡❙♥♠✪❬➅q✻❋✪❢❦❍❡❜❝❋✪❲✝➀ ❪ ❈❊❖❆❋✪❢✵❲❚❙❚❢✵❬③❣■❜❊q✻❋✪❢❦❍❡❜❝❋✪❲✝➀ ➆●❈❊❉❊❋✪➇✵▲✵▼❯❍✦q✻❋✪❢❦❍❡❜❝❋✪❲ ➈✳❈✌❫❥❢❦❍❡❬✎❲❚❲❚❙❚❧✪❬✎❢❦❍➃q✻❋✪❢❦❍❡❜❝❋✪❲✝➀ ❵✝❖❆❬✎▲✵❜❡❣■❲✂❖❆❬⑦❍❥➉✻❋✪❜❝➊❽➋❃⑥✾▲✵➌✎➌⑦P➍q✻❋✪❢❦❍❡❜❝❋✪❲➎➋❽➏✗❬✎❢✵❬⑦❍❡❙❚❑➂➄➃❲❚❧✪❋✪❜❝❙♥❍❡t✵②➐♣ ✈❁✂✰✇✼✾❅✦✽✾❁✂✲ ① ❇
System i odeling based on State ariables 2. Time Domain Design Technique Applicable to I ulti-Input I ulti-Output(IIIO) System 4. arious System Specifications (3) dustec di ecifications for Controller Mesien Stabilit a) Absolute Stability i. All system poles must be in cC ThEC(Re h) Routh-Hurwitz criterion (a)relative Stability vershoot(a5s) dIpr Tracking Capability a)Steady-state t rror r OfTpossible (b) System Type r Optimization (a)Control t nergy minimization (b)Obeect Accomplishment Time minimization
❇✪❈❆⑤❘P●▼❯❍❡❬✎② ❋●❩✵❬✎❲❚❙❚❢✵❧❛➇✾❣■▼❝❬✎❩➍❋✪❢✖⑤❘❍✉❣♦❍❡❬✂✁❹❣■❜❝❙④❣■➇✵❲❚❬✎▼ ◆●❈✌r✌❙❚②✏❬➂❴✦❋✪②❀❣■❙❚❢⑨❴✦❬✎▼❝❙❚❧✪❢✠rs❬✎❑✉t✵❢✵❙❚◗❘▲✵❬ ❳✳❈✌➄➃❞✵❞✵❲❚❙❚❑③❣■➇✵❲❚❬➃❍❡❋ ▲✵❲♥❍❡❙✐❤❥❫❥❢✵❞✵▲✳❍ ▲✵❲♥❍❡❙✐❤❯❶✦▲✳❍❡❞✵▲✳❍❸❵ ❫❶ ♣❊⑤❘P●▼❯❍❡❬✎② ❪ ❈✄✁❹❣■❜❝❙❚❋✪▲✵▼❆⑤❘P●▼❯❍❡❬✎② ⑤●❞❃❬✎❑✎❙✆☎✾❑③❣♦❍❡❙❚❋✪❢✵▼ ★✞✝✻✫✠✟☛✡❆✲❘✼✵❁✌☞ ✟✎✍➅❁✂✶✂✴✑✏➂✶✷✰✇✼✾✴✱✸✻✺✦✲✠✒⑩✸❹✽ ✬✹✸✻✺✻✼✵✽✾✸✻✮❯✮✱❁✂✽✔✓❁✂✲✵✴✖✕✻✺ ❇✪❈❆⑤❘❍✉❣■➇✵❙❚❲❚❙♥❍❥P ❵ ❣❦♣⑨➄➃➇✵▼❝❋✪❲❚▲✳❍❡❬➅⑤❘❍✉❣■➇✵❙❚❲❚❙♥❍❥P ❙➎❈✌➄➃❲❚❲ ▼❯P●▼❯❍❡❬✎② ❞❃❋✪❲❚❬✎▼✌②▲✵▼❯❍❊➇❃❬➂❙❚❢✘✗✚✙✜✛✣✢✥✤✔✦✧✗✩★●❉❊❬✪✤✩✫✭✬✘✮ ❙❚❙➎❈✌❉❊❋✪▲✳❍❡t●❤✖✯❆▲✵❜❯➉❊❙♥❍❡➌❭q✻❜❝❙♥❍❡❬✎❜❝❙❚❋✪❢ ❵ ❣❦♣✠❉❊❬✎❲④❣♦❍❡❙♥♠✪❬❭⑤❘❍✉❣■➇✵❙❚❲❚❙♥❍❥P ❙➎❈❆❶➃♠✪❬✎❜❝▼❝t✵❋●❋■❍❿❵✱✰ ➆✳✲➐♣ ❙❚❙➎❈✌❉❊❙❚▼❝❬➂r✌❙❚②✏❬❛❵✱✰✩✬✵✴ ➆✳✶✞✷✞✸✗♣ ❙❚❙❚❙➎❈✌⑤●❬⑦❍❝❍❡❲❚❙❚❢✵❧❿r✌❙❚②✏❬✏❵✱✰ ◆✹✶✞✷✞✸✗♣ ◆●❈❊❉❊❬✎❧✪▲✵❲④❣♦❍❡❙❚❋✪❢✠❣■❢✵❩✻✺♦❋✪❜✌rs❜❡❣■❑✉➊❘❙❚❢✵❧☎q ❣■❞✾❣■➇✵❙❚❲❚❙♥❍❥P ❵ ❣❦♣➍⑤❘❍❡❬③❣■❩✳P❦❤❥▼❯❍✉❣♦❍❡❬✥✼✝❜❝❜❝❋✪❜ ✽✾✬❛❙✆✿s❞❃❋✪▼❝▼❝❙❚➇✵❲❚❬✗❋✪❜❊❣■▼❊▼❝②❀❣■❲❚❲ ❣■▼❊❞❃❋✪▼❝▼❝❙❚➇✵❲❚❬■❈ ❵ ➇❽♣➍⑤❘P●▼❯❍❡❬✎② r✘P●❞❃❬ ✽ ❳✳❈❆❶✦❞✳❍❡❙❚②✏❙❚➌③❣♦❍❡❙❚❋✪❢ ❵ ❣❦♣➍q✻❋✪❢❦❍❡❜❝❋✪❲❀✼✝❢✵❬✎❜❝❧■P⑨②✏❙❚❢✵❙❚②✏❙❚➌③❣♦❍❡❙❚❋✪❢ ❵ ➇❽♣➍❶✦➇❂❁❝❬✎❑⑦❍❆➄➃❑✎❑✎❋✪②✏❞✵❲❚❙❚▼❝t✵②✏❬✎❢❦❍❊r✌❙❚②✏❬✗②✏❙❚❢✵❙❚②✏❙❚➌③❣♦❍❡❙❚❋✪❢ ❵ ❑ ♣⑨❋■❍❡t✵❬✎❜❝▼ ◆
Example (s)=1/ G(s) r(t)=u(t) 0t
✂✁✰✾☞✍✗✮✱❁❹① G(s) r(s) = 1/s y(s) ✄ ❵✆☎❝♣ ✛✞✝✇❵✆☎❝♣ ✛ ✟✠ ✡ ✠☛ ❇☞☎✞✌ ✬ ✬✍☎✩✫✭✬ ❋☎⑤❘P●▼❯❍❡❬✎② r✘P●❞❃❬ ✛✏✎ Controller 1 s(s+1) r(t) e(t) u(t) plant Type:1 y(t) 1 s setpoint tracking possible ✑✓✒✕✔✖✑✘✗ ✶ ✶ ✛ ✑✘✗✙✔ ✑✓✒ ✶ ❵✣❱✝❫ ❑✎❋✪❢❦❍❡❜❝❋✪❲❚❲❚❬✎❜ ♣ ✚ ⑤●❙❚❢✵❑✎❬✜✛✢ ❬✤✣✳❙❚▼❯❍❡▼❊❙❚❢⑨❍❡t✵❬➂❞✵❲④❣■❢❦❍③➋✳❍❡t✵❬➂❑✎❋✪❢❦❍❡❜❝❋✪❲❚❲❚❬✎❜✌❩✵❋●❬✎▼❊❢✵❋■❍❊t✾❣③♠✪❬➂❍❡❋❛➇❃❬❭❱✝❫✉❈ ❳
*I e can try n+rts( PD controller )or gro( Lead or Lag kts term has the problem of amplifying noise and kt=o is the better choice o Next, consider the canonical or relative stability spec it cation and try to design a controller M) that satisfy the following system specit cations In this case, overshoot
✚ ❬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 ❪
C(s)=l as a simple controller Then the closed loop TF becomes d loop poles the above specs are not met Next, if we apply C(s)=4(s+4) Ge(s C(sG(s) 1+C(sG(s)1+x4 (8+4)832+4s+4 closed loop Poles are S1.2= the above specs are met Next, letr(t)=3 and r(s)=3.Then y(s)=G(s)r(s) lim y(t)=lim sy(s)=lim 0s2+4s+ final value thm This Cl system is able to track the given set-point
✓❀❵ ✶❸♣✾✛ ❇➅❣■▼❊❣❛▼❝❙❚②✏❞✵❲❚❬✦❑✎❋✪❢❦❍❡❜❝❋✪❲❚❲❚❬✎❜✎❈ r✌t✵❬✎❢➍❍❡t✵❬➂❑✎❲❚❋✪▼❝❬✎❩➍❲❚❋●❋✪❞⑨r❊⑥ ➇❃❬✎❑✎❋✪②✏❬✎▼ ✂✁ ❵ ✶❸♣✾✛ ✛ ✢✒✵ ✢✝✆ ✛✝✶ ❇ ✔ ✛ ✢✒✵ ✢✝✆ ✛✝✶ ✛ ❇ ✶ ✏ ✔ ✶ ✔ ❇ ✄ ❍❡t✵❬➂❑✎❲❚❋✪▼❝❬✎❩➍❲❚❋●❋✪❞⑨❞❃❋✪❲❚❬✎▼❊❣■❜❝❬ ✶ ✛✒✬ ✏ ✛ ✭ ❇ ◆ ✰✆☎❳ ◆✞✝ ✄ ❍❡t✵❬ ❣■➇❃❋♠✪❬ ▼❝❞❃❬✎❑✎▼ ❣■❜❝❬ ❢✵❋■❍ ②✏❬⑦❍ ❖❆❬✤✣●❍③➋❽❙✆✿✂➉✻❬➅❣■❞✵❞✵❲♥P ✓❀❵ ✶❸♣✾✛ ❪ ❵ ✢✝✆ ✛ ✢✝✆■♣⑩➋ ✂✁ ❵ ✶❸♣✾✛ ✓❀❵ ✶❸♣ ❵ ✶❸♣ ❇ ✔ ✓❀❵ ✶❸♣ ❵ ✶❸♣ ✛ ✛ ✢✒✵ ✢✝✆✛ ✶ ❇ ✔ ✛ ✢✒✵ ✢✝✆✛ ✶ ✛ ❪ ✶ ✏ ✔ ❪ ✶ ✔ ❪ ✄ ❑✎❲❚❋✪▼❝❬✎❩➍❲❚❋●❋✪❞✠❱s❋✪❲❚❬✎▼❆❣■❜❝❬ ✶ ✛✒✬ ✏ ✛ ✭✦◆✠✟ ✭✦◆ ✄ ❍❡t✵❬ ❣■➇❃❋♠✪❬ ▼❝❞❃❬✎❑✎▼ ❣■❜❝❬ ②✏❬⑦❍ ❖❆❬✤✣●❍③➋❽❲❚❬⑦❍ ✄ ❵✆☎❝♣ ✛ ❳❛❣■❢✵❩ ✄ ❵ ✶❸♣ ✛ ✥ ✢ ❈✝r✌t✵❬✎❢ ➋ ✡ ❵ ✶❸♣ ✛ ✂✁ ❵ ✶❸♣ ✄ ❵ ✶❸♣ ✛ ❇❸◆ ✶❘❵ ✶ ✏ ✔ ❪ ✶ ✔ ❪ ♣ ✄ ❲❚❙❚② ✩☞☛✍✌ ✡ ❵✆☎❝♣ ✛ ❲❚❙❚② ✢☛✏✎ ✶ ✡ ❵ ✶❸♣ ✛ ❲❚❙❚② ✢☛✏✎ ❇❸◆ ✶ ✏ ✔ ❪ ✶ ✔ ❪ ✛ ❳ ❵✚☎✾❢✾❣■❲ ♠■❣■❲❚▲✵❬✦❍❡t✵② ♣ ✄ r✌t✵❙❚▼➃q ❏ ▼❯P●▼❯❍❡❬✎② ❙❚▼❊❣■➇✵❲❚❬✦❍❡❋❿❍❡❜❡❣■❑✉➊❀❍❡t✵❬➂❧✪❙♥♠✪❬✎❢➍▼❝❬⑦❍❯❤❥❞❃❋✪❙❚❢❦❍③❈ ➆