CHEN 4601 Lecture Notes - Lecture 27: Paga
22 Oct 2015
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The poles of the closed-loop transfer functions are the roots of. This is proportional controller this makes it unstablepositive pole. -> can"t physically operate this system without it going bananas. If kc > 2/5 -=> p < 0 the system will be stable if you make kc large enough example 2. Chen4601_processcontrol page 1 proportional controller not putting km here b/c it = 1 static gain = 1 characteristic eqn. Examples 1 and 2 shows that open loop doesn"t determine closed-loop stability or vice versa also, control paraemters affect closed-loop stability; poor choice can make a stable system to be have in an unstable manner in closed-loop. Yes --> called the routh-herwitz criterion (they developed it independently) --> a purely algebraic method for determining how many roots of a polynomial have positive re parts n = # poles. If any coefficient is negative or zero, then there is at least one root w/ positive or zero re part => unstable.
