study brief, intelligible, and loop unit step responses of the nominal plant and I CONTROL PROBLEM the two perturbed plants. To be acceptable, th closed loop step resp onses must simultaneously have A. Motor Speed contro short rise time an Motivated by the work in [o] and [ol, and encour- F. Design approach aged by the robustness results presented for fuzzy logic control, we consider the robust speed control We design the fuzzy, PID, and sliding mode con trollers based on the nominal plant given in equa- time-invariant transfer function. The general con- tion(1 ) Each designed controller is then applied figuration for the motor speed control problem is to all three transfer functions and numerical sim given in Figure 1 ulations are performed to analy ze the controller The design of the fuzzy logic controller is given Controller- in Section IV. The design of the PID controller is given in Section V. The design of the sliding mode controller is given in Section VI. Plots of each con- troller's closed e and control effor are shown in Appendix A Figure 1: Motor Speed Control Problem IV, ANALYSIS AND RECONSTRUCTION OF A Fuzzy RoI We use the nominal plant, perturbed motor plants, We implement the robust fuzzy controller given in and the performance criteria given in [] to design [o] and [0]. The inputs to the fuzzy controller are e and compare robust fuzzy, PID, and sliding mode and we. The output of the fuzzy controller controllers universes of discourse of e, wc, and u are partitioned B.Restrictions on Controller Inputs and Outputs Into seven As shown in Figure 1, the reference step input speed NB- negative big nd the out put motor speed wc are available fo ·NM- negative mediun parison. Each controller only has access to the Ns-negative small motor speed error e =Wr-wc and the motor angular ZE -zero acceleration wc as inputs. Each controller produces PS- positive small only one output u ●PM- positive mediun C. Nominal plant The nominal motor plant is modeled by the follow Each fuzzy set is represented by a Gaussian men ing transfer function bership function. The rule base of the fuzzy logi controller contains forty-nine rules which are tabu- lated in Figure 2. The output of each rule is de- (1) termined by min-inference. The crisp output u of the fuzzy logic controller is generated by centroid D. Perturbed plants The two perturbed motor plants are given by the fo llowing transfer functions ZE NB NM NS PS PM PB (s) (2) NS ZE PM PB PB PB PB PB NB ZE PS PM PBPBPBPB G3(s) Figure 2: Fuzzy Logic Controller Rule Base E. Perform ane The designed controllers must be robust to varia- The step response of this fuzzy logic controller ap tions of system parameters. Specifically, for the plied to the nominal and perturbed plants is shown fuzzy logic, PID, and sliding control designs, one in Appendix A. The step responses for all three single controller must render acceptable the closed plants have short rise times and no overshoot. Thusé➃õ②ê❑ú◆ñ④✑❉ö➃ó➪è❾í❚✲◆ó➪ô◆õ②è✉î➪î➪ó➪ò➍ó✄✑❉î➪è☛✲➍÷➁ô❑ú✱✡❳è❫÷➁ô❉ó➪ô❉òrí❇ê❃î ✝ ➱s➱✉➱❫✃✧⑤➬❰ ❐q❒q❮❰❶⑩✁￾■❮❰✄✂✦⑩✬⑦✆☎ Ó❝Ô✞✝✍Ù❅Û②ÙrÜ✠✟☛✡➡Ö❾Ö✣✥❚Ø✐Ù➁Ú◆Û❤Ü➏ÙrÝ ☞❚ï❢õ②ó✄✎➍÷rõ➃è❫ú✵✑◆ñ✍õ➃ç❉è❳ü■ï➍ö✳❀✍ó➪ô✣þÿ✁ ÷rô❑ú❴þÿ✁ ✲➘÷➁ô❑ú✚èsô❑ë❾ï➍ê❃ö✗✟ ÷➁ò➍è❫ú ✑❵ñ✼õ②ç❃è❳ö②ï✬✑❉ê❉é➃õ②ô❉è✉é➃é❳ö➃è✉é②ê❉î➪õ➃é✇ù❉ö➃è✉é②èsô❵õ➃è❫úâí❇ï❢ö❥í❇ê❉ðsð✉ñ î➪ï➍ò❢ó①ë✇ë❾ï❢ô◆õ②ö②ï❢î✗✲qü✐è❳ëìï➍ô❉é➃ó ú➡è✉ö✿õ②ç❃è❳ö②ï✬✑❉ê❉é➃õ✿é②ù❭è✉è❫úâë❾ï➍ô◆õ②ö➃ï➍î ï➁í➘÷❥ö②ï❢õ➏÷rõ➃ó➪ô❉ò❯✡❳ï➍õ➃ï➍ö✏✲✓✡❳ï❉ú◆è✉î➪è❫út✑◆ñ✈÷❞õ②ç❉ó➪ö➏ú④ï❢ö➏ú◆èsö✐î➪ó➪ô❉è❫÷➁ö õ➃ó✩✡➲è✣✟❤ó↕ô✠✎➍÷➁ö②ó①÷rô◆õ➳õ➃ö➏÷➁ô❉é❤í❇èsö✿í❇ê❃ô❑ë❾õ②ó➪ï❢ô ✝ æ➹ç❉è➲ò➍è✉ô❃è✉ö➏÷➁î ë❾ï❢ô✠✟ ✌ò❢ê❉ö➏÷➁õ②ó➪ï➍ôâí❇ï❢ö❳õ➃ç❉è✾✡❳ï❢õ②ï❢ö✇é➃ù❑è✉è❅ú✜ë❾ï➍ô◆õ②ö➃ï➍î❍ù❉ö②ï✬✑❉î➪è✞✡✞ó➪é ò❢ó✩✎❢è✉ô❚ó➪ô s❬ó➪ò➍ê❉ö➃è✎✍ ✝ . r c c e y ω ω ω - + s Plant Motor Controller s❬ó➪ò➍ê❉ö➃è✏✍☛✑✒☞❚ï➍õ➃ï➍ö ✯ ù❭è✉è❫ú✔✓■ï❢ô◆õ②ö②ï❢î❲❺✌ö②ï✬✑❉î➪è✞✡ ✇è✌ê❉é②è➋õ②ç❉è✹ô❃ï☛✡❳ó➪ô❑÷➁î✉ù❉î①÷rô◆õ✏✲✉ù❭è✉ö②õ➃ê❉ö❈✑❭è❫ú✧✡❳ï❢õ②ï❢ö❉ù❉î①÷rô◆õ②é✏✲ ÷➁ô❑ú✙õ➃ç❉è❋ù❭è✉ö❤í❇ï❢ö❈✡❚÷rô❑ë❾è❳ëìö②ó➪õ②è✉ö➃ó①÷❳ò❢ó✄✎➍è✉ô✼ó➪ô þÿ✁ õ➃ï➐ú➡è✉é②ó➪ò➍ô ÷➁ô❑ú☛ë❾ï✬✡❳ù❑÷➁ö②è❋ö➃ï☛✑❉ê❉é➃õ✿í▲ê❉ð✉ð✉ñ✠✲✖❺❣✼❈❻✧✲➘÷➁ô❑ú✚é➃î➪ó ú➡ó↕ô❃ò ✡➲ï❉ú◆è ë❾ï❢ô◆õ②ö②ï❢î➪î↕èsö②é ✝ ✙Ô☞✉➹Ö❾ß❾Û❤Ü✉ä✆❥ìÛ➶ä❇Ù➁Ú◆ß✇ÙrÚ✚Ø✐Ù➁Ú◆Û❤Ü➏ÙrÝ Ý↕ÖsÜ✖✕sÚ✗✡✦✈❢Û▲ß❦✢rÚ✦✥✙✘❵✈❢Û✚✡❅✈➍Û▲ß ★é✹é②ç❉ïrü➹ô④ó➪ô❦s❬ó➪ò➍ê❉ö➃è✛✍✬✲rõ②ç❉è■ö②èìí❇è✉ö②èsô❑ë❾è➳é➃õ②è✉ù❋ó➪ô❉ù❃ê❉õ✌é②ù❭è✉è❫ú ✜✒✢ ÷rô❑úûõ②ç❉è❝ï➍ê❉õ➃ù❉ê❉õ❵✡❳ï❢õ②ï❢ö✐é➃ù❑è✉è❅ú ✜✤✣ ÷rö②è④÷✏✎➍÷ró➪î①÷✓✑❉î➪è■í❇ï❢ö ë❾ï✬✡❳ù❑÷➁ö②ó➪é②ï❢ô ✝✦✥÷➍ë➃ç✚ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö❍ï➍ô❉î➪ñ❳ç❭÷ré➬÷❢ë✉ë❾è✉é➃é✿õ②ï➲õ②ç❉è ✡➲ï➍õ②ï❢öqé②ù❭è✉è❫ú❝è✉ö②ö➃ï➍ö✤✧✩★ ✜✪✢✬✫✦✜✤✣ ÷➁ô❑ú❥õ➃ç❉è✖✡❳ï❢õ②ï❢ö ÷➁ô❉ò➍ê❉î①÷➁ö ÷❢ë✉ë❾è✉î➪è✉ö❾÷rõ②ó➪ï❢ô✮✭ ✜ ✣ ÷ré➹ó➪ô❉ù❉ê❉õ➃é ✝✯✥÷➍ë➃ç✍ë❾ï❢ô◆õ②ö②ï❢î➪î↕èsö➹ù❉ö②ï❉ú◆ê❑ëìè✉é ï❢ô❉î➪ñ❋ï➍ô❉è❥ï➍ê❃õ②ù❉ê❉õ✱✰ ✝ Ø✹Ô❝Õ❞Ù➁ã✇ä①Ú❅✢rÝ❂✐■Ý✩✢rÚ➡Û æ➹ç❉è❝ô❉ï☛✡➲ó↕ô❭÷rî②✡➲ï➍õ②ï❢ö✐ù❃î ÷➁ô◆õ✐ó➪é❵✡❳ï❉ú◆èsî↕è❅ú✤✑◆ñ❳õ➃ç❉è❥í❇ï❢î↕î➪ïrü✽✟ ó➪ô❉ò④õ②ö❾÷rô❉é➔í❇è✉ö➹í▲ê❉ô❑ë❾õ➃ó↕ï❢ô✲✑ ✳ ❭ ý✵✴ ☎ ★ ✶ ✴➁ý✷✴✯✸✹✍ ☎ ý✵✴✺✸✼✻ ☎ ý✽✍ ☎ ✚❥Ô✧✐Ö✉ÜìÛ❹✈◆Ü✜✛❾Ö✣✥t✐✐Ý✩✢➁Ú◆Û▲ß æ➹ç❉è❚õ❤ü■ï✍ù❭è✉ö➃õ②ê❉ö✳✑❑è❫ú ✡❳ï➍õ➃ï➍ö✿ù❃î ÷➁ô◆õ②é❋÷rö②è➲ò➍ó✄✎➍èsô ✑◆ñ✚õ②ç❉è í❇ï❢î➪î↕ïrü➹ó➪ô❉ò❝õ②ö➏÷➁ô❉é❤í▲è✉ö■í❇ê❉ô❑ëìõ②ó➪ï➍ô❉é✾✑ ✳✞✿ ý✵✴ ☎ ★ ✍ ✶ ✴➁ý✷✴✯✸✹✍ ☎ ý✵✴✺✸✼✻ ☎ ý✵✻ ☎ ✳✱❀ ý✵✴ ☎ ★ ✶ ✴ ✿ ý✵✴✺✸❁✻ ☎ ý✵❂ ☎ á✐Ôt✐ÖsÜ✍✹❫Ù➁Ü✉ã ✢➁Ú✦❥❾Ö❋Ø✹Üsä➪Û➔ÖsÜ✉ä✆✢ æ➹ç❉è✙ú◆èsé②ó➪ò➍ô❉è❅ú✣ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö➃é❦✡❋ê❉é➃õ❦✑❭è❚ö②ï✬✑❉ê❉é②õ❋õ➃ï⑨✎➍÷rö➃ó ÷✟ õ➃ó↕ï❢ô❉é✙ï➁í❳é②ñ◆é②õ➃è✞✡✴ù❑÷rö❾÷✓✡❳èsõ②è✉ö➃é ✝ ✯ ù❭è❫ë❾ó✌ë✉÷➁î➪î↕ñ✠✲❍í❇ï❢ö✙õ②ç❉è í❇ê❃ð✉ð✉ñ✣î➪ï➍ò❢ó①ë✓✲❵❺❣✼❈❻✧✲✐÷rô❭ú❴é②î➪ó①ú◆ó➪ô❉ò✚ë❾ï➍ô◆õ②ö➃ï➍î✿ú◆è✉é➃ó➪ò➍ô❉é✏✲➹ï➍ô❉è é➃ó↕ô❃ò➍î➪è✈ëìï➍ô◆õ②ö➃ï➍î➪î➪è✉ö☞✡❋ê❉é➃õ➳ö②èsô❑ú◆è✉ö❋÷➍ë✉ëìè✉ù❉õ➏÷✔✑❉î➪è❋õ②ç❉è❳ëìî↕ï❢é②è❫ú î➪ï◆ï➍ù✚ê❉ô❉ó➪õ✿é➃õ②è✉ù❴ö➃è✉é②ù❭ï➍ô❉é➃è✉é❋ïrí➳õ➃ç❉è❳ô❃ï☛✡❳ó➪ô❑÷➁î✌ù❉î①÷rô◆õ✇÷rô❭ú õ②ç❃è✍õ❤ü■ï☛ù❭è✉ö②õ➃ê❉ö❈✑❭è❫ú❙ù❉î①÷➁ô❵õ➃é ✝ æ✌ï⑨✑❑è✚÷➍ë✉ëìè✉ù❉õ➏÷✔✑❉î➪è☛✲❍õ②ç❉è ë❾î➪ï➍é➃è❫ú❝î↕ï◆ï❢ù✿é②õ➃è✉ù✇ö➃è✉é②ù❭ï➍ô❃é②è✉é✽✡❋ê❉é②õqé➃ó✄✡❋ê❉î➪õ➏÷rô❃è✉ï➍ê❉é➃î➪ñ➳ç❑÷✏✎❢è é②ç❃ï➍ö②õ❍ö②ó➪é②è❥õ➃ó✩✡➲è➬÷➁ô❑ú➲ô❉ï✇ï✓✎❢è✉ö②é➃ç❉ï◆ï➍õ ✝ ♥✹Ô✧✚❞Öìß✉ä✄✸❱Ú➲Ó✦✡☛✡❭Ü➏Ù✏✢☛❥❝✺ ✇è✙ú◆è✉é➃ó↕ò❢ô✣õ②ç❃è❚í❇ê❉ð✉ðsñ❞✲❵❺❣✼❈❻✧✲✹÷rô❭ú☛é➃î➪ó ú➡ó↕ô❃ò③✡➲ï➡ú➡è➐ëìï➍ô✠✟ õ②ö➃ï➍î➪î➪è✉ö②é✧✑❑÷➁é②è❫ú✼ï❢ô✚õ②ç❉è❋ô❉ï✬✡❳ó➪ô❑÷➁î➘ù❃î ÷➁ô◆õ➬ò❢ó✄✎➍è✉ô✼ó➪ô✚è✜✌❢ê❑÷✏✟ õ②ó➪ï❢ô✣ý❃✍ ☎✞✝❄✥÷❢ë②ç✣ú◆èsé②ó➪ò➍ô❉è❅ú ëìï➍ô◆õ②ö➃ï➍î➪î➪è✉ö✇ó➪é④õ②ç❉èsô ÷rù❃ù❉î➪ó↕è❅ú õ②ï✚÷rî➪î✹õ➃ç❉ö②èsè❳õ②ö❾÷rô❉é➔í❇è✉ö④í❇ê❃ô❑ë❾õ②ó➪ï❢ô❉é✜✲✌÷rô❑ú ô◆ê②✡❳è✉ö➃ó①ë✉÷rî✌é②ó✄✡❽✟ ê❉î①÷rõ➃ó➪ï➍ô❉é❳÷➁ö②è✼ù❑è✉ö➔í❇ï➍ö✳✡❳è❫úâõ➃ï ÷rô❭÷rî➪ñ◆ð✉è❚õ②ç❉è✚ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö✾❅ é ö②ï✬✑❉ê❉é➃õ②ô❉è✉é➃é ✝ æ➹ç❉è➮ú➡è✉é②ó➪ò➍ôâïrí➳õ➃ç❉è➲í❇ê❉ð✉ð✉ñ✚î➪ï❢ò➍ó①ë❋ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö④ó➪é✿ò➍ó✄✎➍èsô ó➪ô ✯ è❫ë❾õ②ó➪ï❢ô⑨✼✵❆ ✝ æ➹ç❉è❳ú➡è✉é②ó➪ò➍ô✚ï➁í✐õ②ç❃è✘❺❣✼❈❻✮ë❾ï❢ô❵õ➃ö②ï❢î↕î➪è✉ö❝ó↕é ò➍ó✄✎❢è✉ô✙ó➪ô ✯ è❫ë❾õ➃ó↕ï❢ô✔❆ ✝ æ➹ç❉è✇ú◆èsé②ó➪ò➍ô✙ï➁í✹õ②ç❉è✿é➃î➪ó ú➡ó↕ô❃ò✤✡❳ï❉ú◆è ë❾ï❢ô❵õ➃ö②ï❢î↕î➪è✉ö❍ó➪é➹ò➍ó✄✎➍è✉ô➲ó➪ô ✯ è❫ë❾õ②ó➪ï❢ô✔❆✫✼ ✝ ❺✌î➪ï➍õ➃é➹ïrí✹è❫÷➍ë➃ç✍ëìï➍ô✠✟ õ②ö➃ï➍î➪î➪è✉ö❇❅ é➹ë❾î➪ï➍é➃è❫ú➲î↕ï◆ï❢ù❋é②õ②èsù➮ö➃è✉é②ù❭ï➍ô❃é②è✿÷rô❑ú➲ë❾ï➍ô◆õ➃ö②ï➍îqè❉❈ï❢ö②õ ÷rö➃è✿é②ç❃ïrü➹ô➮ó➪ô ★ù❉ù❭è✉ô❑ú◆ó➟ø ★ ✝ ➱❋❊➮✃✱●❝❐■❍❂⑩✽❏❸sÒ✆❸✏❍q❐qÏ▲❑✿⑦❑Ñq❰q❐❲❸s❒q❮❑Ð❨Ñ❭❒qÒ▲❰q❐ ❰❶⑧✔❍ ▼✹Ð✲◆☛◆❖❏✹❑➳❰■✂❭Ð❲❸✉❒ ⑤➬❰q❐q❒q❮q❰❂⑩✬⑩☛⑦❉❮ ✇è④ó✩✡➲ù❉î➪è✞✡❳èsô❵õ➹õ➃ç❉è❋ö②ï✬✑❉ê❉é➃õ❥í❇ê❉ð✉ðsñ ë❾ï❢ô◆õ②ö②ï❢î➪î↕èsö➬ò❢ó✄✎➍è✉ô✼ó➪ô þÿ✁ ÷➁ô❑ú✼þÿ✁❈✝ æ➹ç❉è❝ó↕ô❃ù❉ê❉õ②é➹õ➃ï❋õ②ç❉è❍í❇ê❃ð✉ð✉ñ✙ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö➳÷➁ö②è✞✧ ÷rô❭ú✹✭ ✜ ✣ ✝ æ➹ç❉è➹ï❢ê❉õ②ù❉ê❃õ➘ï➁í õ➃ç❉è■í❇ê❉ðsð✉ñ✇ë❾ï❢ô❵õ➃ö②ï❢î↕î➪è✉ö✌ó➪é✤✰ ✝ æ➹ç❉è ê❉ô❉ó✄✎❢è✉ö②é➃è✉é✐ï➁í ú➡ó↕é❾ë❾ï➍ê❃ö②é②è❍ïrí✲✧☛✲P✭ ✜ ✣ ✲❵÷➁ô❑ú◗✰❋÷rö②è➹ù❭÷rö②õ➃ó➪õ②ó➪ï➍ô❉è❅ú ó➪ô◆õ②ï❋é②è✮✎➍è✉ô❚í▲ê❉ð✉ð✉ñ➲é②è✉õ➃é❇✑ ❘ ✕✩❙ ✟✐ô❃è✉ò❵÷➁õ②ó✄✎➍è✿✑❉ó➪ò ❘ ✕☞ ✟✹ô❉è✉ò❵÷➁õ②ó✄✎➍è❯✡➲è❫ú◆ó➪ê②✡ ❘ ✕✯ ✟✹ô❉è✉ò❵÷➁õ②ó✄✎➍è❥é✳✡➮÷rî➪î ❘❁❚ ✥ ✟■ð✉è✉ö②ï ❘ ❺ ✯ ✟❁ù❭ï➍é➃ó➪õ②ó✄✎➍è❥é❈✡❚÷rî➪î ❘ ❺✤☞ ✟❁ù❭ï➍é➃ó➪õ②ó✄✎➍è❯✡❳è❅ú◆ó➪ê②✡ ❘ ❺ ❙ ✟✐ù❭ï➍é➃ó↕õ➃ó✄✎➍è✫✑❃ó↕ò ✥÷❢ë②ç✼í▲ê❉ð✉ð✉ñ✼é②è✉õ④ó➪é❥ö②è✉ù❉ö➃è✉é②èsô❵õ➃è❫ú✰✑◆ñ✍÷❱❯✿÷rê❉é➃é②ó①÷rô✵✡❳è✮✡✤✟ ✑❭è✉ö②é➃ç❉ó➪ù☛í▲ê❉ô❑ë❾õ➃ó↕ï❢ô ✝ æ➹ç❉è➲ö②ê❉î➪è✤✑❑÷➁é②è❳ï➁í➳õ②ç❉èûí❇ê❉ð✉ðsñ✚î↕ï❢ò➍ó①ë ë❾ï❢ô❵õ➃ö②ï❢î↕î➪è✉ö✿ë❾ï❢ô◆õ➏÷ró➪ô❉é í❇ï➍ö➃õ❤ñ✬✟➶ô❉ó➪ô❉è❥ö➃ê❉î➪è✉é❥ü➹ç❉ó①ë②ç✼÷rö②è④õ➏÷✔✑❉ê✠✟ î①÷rõ➃è❫úâó↕ô s❬ó↕ò❢ê❉ö②è❱✻ ✝ æ➹ç❉è❚ï➍ê❉õ➃ù❉ê❉õ④ïrí❥è❫÷➍ë➃ç❴ö②ê❉î➪è❚ó➪é✈ú➡è✣✟ õ②èsö❈✡❳ó➪ô❉è❅ú⑨✑◆ñ③✡➲ó➪ô✠✟➶ó➪ô◆í▲è✉ö②è✉ô❭ë❾è ✝ æ➹ç❉è❚ë❾ö②ó➪é②ùâï➍ê❉õ➃ù❉ê❉õ✏✰✚ï➁í õ②ç❃è❚í❇ê❉ð✉ðsñ☛î➪ï➍ò❢ó ë➲ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö④ó➪é❋ò➍è✉ô❉èsö➏÷rõ➃è❫ú ✑◆ñ☛ë❾è✉ô◆õ➃ö②ï➍ó①ú ú◆è❾í▲ê❉ð✉ð✉ó✌ë✉÷➁õ②ó➪ï➍ô ✝ ❲ ❳✲❨ ❳✲❩ ❳✪❬ ❭☛❪ ❫■❬ ❫❴❩ ❫❴❨ ❫❵❨ ❳✲❨ ❳✲❨ ❳✲❨ ❳❛❨ ❳❛❩ ❳✪❬ ❭❜❪ ❫❵❩ ❳✲❨ ❳✲❨ ❳✲❨ ❳✲❩ ❳✪❬ ❭❜❪ ❫❝❬ ❫■❬ ❳✲❨ ❳✲❨ ❳✲❩ ❳✪❬ ❭❜❪ ❫■❬ ❫❵❩ ❡✆❢ ❞ ❭❜❪ ❳✲❨ ❳✲❩ ❳✪❬ ❭☛❪ ❫■❬ ❫❴❩ ❫❴❨ ❳✒❬ ❳✲❩ ❳✪❬ ❭❜❪ ❫■❬ ❫❴❩ ❫❵❨ ❫❴❨ ❳❛❩ ❳✒❬ ❭❜❪ ❫■❬ ❫❴❩ ❫❵❨ ❫❵❨ ❫❴❨ ❳✲❨ ❭❜❪ ❫■❬ ❫❵❩ ❫❴❨ ❫❵❨ ❫❵❨ ❫❴❨ s❬ó➪ò➍ê❉ö➃è✠✻❣✑✖s❉ê❃ð✉ð✉ñ✐❤ ï➍ò❢ó ëP✓■ï➍ô◆õ②ö➃ï➍î➪î➪è✉ö✩❥➹ê❃î↕è ❙ ÷➁é②è æ➹ç❉è■é②õ②èsù✇ö➃è✉é②ù❭ï➍ô❉é➃è➹ïrí❑õ➃ç❉ó➪é❬í❇ê❉ð✉ð✉ñ❥î➪ï➍ò❢ó①ë✹ë❾ï➍ô◆õ➃ö②ï➍î➪î➪è✉ö✌÷rù✠✟ ù❉î➪ó➪è❫ú➲õ②ï④õ②ç❉è❥ô❉ï✬✡❳ó➪ô❑÷➁î➡÷➁ô❑ú➲ù❑èsö②õ②ê❃ö❈✑❭è❫ú❚ù❉î①÷rô◆õ➃é✐ó➪é➹é②ç❃ïrü➹ô ó➪ô ★ù❃ù❑è✉ô❭ú◆ó➟ø ★ ✝ æ➹ç❃è✙é②õ➃è✉ù✦ö➃è✉é②ù❭ï➍ô❃é②è✉é❚í▲ï➍ö➮÷➁î➪î➹õ②ç❉ö➃è✉è ù❉î①÷rô◆õ➃é❨ç❑÷✏✎❢è✐é➃ç❉ï➍ö➃õ❨ö②ó➪é➃è✐õ➃ó✩✡➲è✉é➘÷➁ô❑ú❥ô❉ï❍ï✓✎➍è✉ö➃é②ç❉ï◆ï❢õ ✝ æ➹ç❵ê❃é✜✲