Could you please solve it step by step and fast I have 30 minutes

For this system, it is desired to design a state feedback control system that meets the following criteria. Status feedback will be done through the observer.

i-Unit digit response steady state error must be zero.

ii-Unit step response should have a maximum overflow amount of 4.3%.

iii- Unit step response sitting time (for 2% band) should be at most 2 seconds. The region where the roots should be in order to meet the criteria given for the transient response is shown in the complex plane as shown in the figure. Accordingly,

a) Design a state feedback control system that meets all the criteria for this system using Ackerman's formula.

b) Design an observer for this system. Use the Bass-Gura v method for the observer design.

c) Draw the block diagram of the control system including the observer you designed in a and b.

d) Find the state-space model of the system you designed.
 

E-PAC-8. * = [ ] [ 2 ] + y= = Bu sistem iin aada verilen kstaslar salayan bir durum geri besleme kontrol sistemi tasar- lanmak istenmektedir. Durum geri beslemesi gzleyici zerinden yaplacaktr. i-Birim basamak cevabi kalc durum hatas sfr olmaldr. i-Birim basamak cevab maksimum tama miktar en fazla %4.3 olmaldr. iii-Birim basamak cevab oturma zaman (2 lik band iin) en fazla 2 saniye olmaldr. Geici durum tepkisi iin verilen kstaslarn salanabilmesi iin kklerin olmas gereken blge karmak dzlemde ekildeki gibi gsterilmitir. Buna gre, (20p) a) Bu sistem iin verilen tm kstaslar salayan bir durum geri besleme kontrol sistemini Ackerman formuln kullanarak tasarlaynz. (10p) b) Bu sistem iin bir gzleyici tasarlaynz. Gzleyici tasarm iin Bass-Gura yntemini kul- lannz. (10p) c) a ve b klarnda tasarladnz gzleyici ieren kontrol sisteminin blok emasn iziniz. (10p) d) Tasarladnz sistemin durum-uzay modelini bulunuz. stenilen Blge -2 45 45 jw