Fal!2001 16.3118-9 ● Can use“ closeness”ofL(s) to the critical point as a measure of closeness"to changing the number of encirclements Premise is that the system is stable for the nominal system has the right number of encirclements e goal of the robustness test is to see if the possible perturbations to our system model(due to modeling errors)can change the number of encirclements In this case, say that the perturbations can destabilize the system Nichols: U Phase(deg) Figure 5: Nichols Plot for the cart example which clearly shows the sensitivity to the overall gain and or phase lagFall 2001 16.31 18—9 • Can use “closeness” of L(s) to the critical point as a measure of “closeness” to changing the number of encirclements. — Premise is that the system is stable for the nominal system ⇒ has the right number of encirclements. • Goal of the robustness test is to see if the possible perturbations to our system model (due to modeling errors) can change the number of encirclements • In this case, say that the perturbations can destabilize the system. −260 −240 −220 −200 −180 −160 −140 −120 −100 10−1 100 101 Nichols: Unstable Open−loop System Mag Phase (deg) −180.5 −180 −179.5 −179 −178.5 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 Nichols: Unstable Open−loop System Mag Phase (deg) 1 0.99 1.01 Figure 5: Nichols Plot for the cart example which clearly shows the sensitivity to the overall gain and/or phase lag