CONTROL SYSTEM DESIGN Lecture Notes Robust Control Systems Page r - Sr  i : ri is the ith root i  /  n - ST   i 1 n - ST   i 1 10 11 12 14 Sri s  ri : if zeros of T(s) are independent of the parameter α Sri s  ri : relationship of two sensitivities - This system is not very robust - This is a PD controller - This system is not very robust - Gm(s): a multiplicative perturbation - M ( j )   15 16 17 19 Notes Gc ( j )G ( j ) for all  : assume that G & Gm have the same number of poles in the right-hand s-plane - If K = 1, the system is unstable - Gm (s)  G(s)[1  M (s)] : the process G becomes Gm - M ( j )   Gc ( j )G ( j ) for all  : condition for a stable system - sn  an1sn1  an2 sn2   a0  : the characteristic equation q1 (s)  s3   s  1s  0 - q2 (s)  s3  2 s  1s  0 q3 (s)  s3  2 s  1s  0 : possible characteristic equations when coefficients q4 (s)  s3   s  1s  0 20 22 24 change - According to Routh – Hurwitz criterion, this system is stable - q(s)  s3  3s  2s  4.5  : the nominal characteristic equation - T (s)  Y (s)  1: R( s ) one possible objective in the design of a control system is that 28 the controlled system's output should exactly and instantaneously reproduce its input That is, the system transfer function should be unity - Gp (s) : the prefilter 30 - s3  1.75n s2  2.15n2 s  n3 : see page #46, Performance of FCS 1    Page Notes 32 - Percent overshoot is not very good, then a prefilter is required 36 - This system is very stable 39 - K = 0: no state variable feedback - s2  3.2n s  n2 : see page #47, Performance of FCS 40 - Suppose that settling time is second 41 - This system is very stable 42 - Poles can change by 50% 43 - Table: see page #53, Design of FCS - Suppose that Ka = 10, Kb = 44 - This system is very stable 2    ...Page Notes 32 - Percent overshoot is not very good, then a prefilter is required 36 - This system is