Name of the student exercise 1 (15pts t f a stable system is a dynamic system with a bounded output response t f the routh-hurwitz criterion is a necessary and sufficient criterion for t f auxiliary polynomial is the equation that immediately precedes the zero entry in determining the stability of linear systems the routh array. it is used to the singularities located symmetrically about the s- plane origin t f ziegler-nicholas pid tuning method refers to the process whereby, the pid control gains are obtained by trial-and-error with minimal analytic analysis based on open loop or closed-loop step response the number of separate root locus section in the s-plane is equal the number of zeros of the transfer function t f t f asystem is stable if all poles lie ia the right half side of the s-plane the breakaway point is the root locus, crossover point on the imaginary axis of the s-plane t f t f gain margin is measured at the gain crossover frequency t f the close loop control system is stable if the gain margin is negative t f phase margin is measured at the phase crossover frequency t f phase margin is the additional drop in phase angle that can be added to open- loop before the corresponding close-loop becomes unstable a close loop control system is stable if the open-loop phase angle crosses-180 t f when its gain is greater than 1 in the s-plane, the root locus evolves from the zeros towards the poles. inarouth array, the system stability is asserted by visiting the change of sign in t f t f the first row the gain margin of a system is the increase in the system gain when the phase is t f -180° that will result in a marginally stable system.