Fal!2001 16.3118-5 Freq(rad/sec) Figure 3: Loop and margins Looking at both the Loop plots and the root locus, this system is stable with a gain of 1, but Unstable for a gain of 1+e and or a slight change in the system (possibly due to some unmodeled delays Very limited chance that this would work on the real system Of course, this is an extreme example and not all systems are like this, but you must analyze to determine what robustness mar gins your controller really ha Question what analysis tools should we use?Fall 2001 16.31 18—5 10−2 10−1 100 101 102 10−2 10−1 100 101 Freq (rad/sec) Mag Loop L 10−2 10−1 100 101 102 −300 −250 −200 −150 −100 Freq (rad/sec) Phase (deg) Figure 3: Loop and Margins • Looking at both the Loop plots and the root locus, this system is stable with a gain of 1, but — Unstable for a gain of 1±² and/or a slight change in the system phase (possibly due to some unmodeled delays) — Very limited chance that this would work on the real system. • Of course, this is an extreme example and not all systems are like this, but you must analyze to determine what robustness mar￾gins your controller really has. • Question: what analysis tools should we use?