Question

A Calculator is allowed. Question 7: The following transfer function is unstable. H(s) = ! Explain why the function is unstable. Plot any existing poles and zeros on the complex (s-domain) plane. Find a feedback method (P,D, or Ior any summative combination of P, D, or I) to make the system stable. Prove it is stable mathematically.

Answer 1

lut e H(S) = 's + dibeberent type of stability :- tz Ab sealedy Slable system 4 BI BO stable. pole lies left af half absolute stable S plane the JW ** Cibility from polt) x x (pole-Zero polts Slable s- plone margenal Slable Repeate root on peper Repeate root im-axis at ongen o anotable. given fan ers) = of one pole at origen we can say of io marigenal stable

1. Can be svolem . This treate but as per control as absolute statable System Life Const it flos) = 0 < to a.s. ) Exo I stable - It fle) o g a to BI BO Stability C Bounded if Bounded out ped) XS [46) } yes) let in pod is slep from X (f) = u(e) e Bounded X(s) = 5, 4(S) = Vs y = 5 5 = /2 y(t) = A ace) Bystern Cis. Lit YCC) =of E ² Hes) y) = EUCE), Cece T Bounde « BI BO unstable anBounded 06 - say an so we can system is unstable "BIBO"

HIS) = ls 2 pole gero polt limis) onle one pole cet origen ③ here you asked to use PD (or) I Contoolley but = the system which have type 32 ftype 0, 13; are basically stable." By applying proper Gud back, we can make system stable - with out Controlles (or) Compensator. to the system tot apply unit feed back 74 = firme care

System is absolute stable pole are at L-H absolute stable - let check BIBO XC6) = u(t) ys) = c(3) = x(s):7/5) - šist) = Ś it'90)= y(e)= (-ė gece) f system stable 4 YCE) =o GAP Control (kp o) - No-need let case propertion (G) y a use & Ekp I use controller mis al mead - Stable Ke open loop Tif = GHCS) = Helyko a as kott pole moving poanrd LHS. - systemis Relatively root locase more stable"