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Chapter 4 Controller Synthesis
MATRIXx Xmath Robust Control Module 4-22 ni.com
10. Compute the closed-loop system for the reduced order plant and the
frequency-shaped compensator:
[Sysfs_scl]=feedback(Sysr,Sysfs_sc);
poles(Sysfs_scl)
ans (a column vector) =
-0.645263 + 0.587929 j
-0.645263 - 0.587929 j
-0.500025 + 0.866011 j
-0.500025 - 0.866011 j
-0.347592 + 1.09155 j
-0.347592 - 1.09155 j
11. Compute the closed-loop system for the full-order plant and the
frequency-shaped compensator.
Sysfs_scl_fo = feedback(Sys,Sysfs_sc);
poles(Sysfs_scl_fo)
ans (a column vector) =
-0.690216 + 0.522898 j
-0.690216 - 0.522898 j
-0.419783 + 0.892632 j
-0.419783 - 0.892632 j
-0.381722 + 1.10668 j
-0.381722 - 1.10668 j
-0.0261589 + 5.00027 j
-0.0261589 - 5.00027 j
The full-order closed-loop system is stable. The open-loop eigenvalues
of the unmodelled mode have not moved much, which is a sign of good
robustness. The eigenvalue of the unmodelled mode changed from
–.0250 ± 5j to –0.0262 ± 5j.
Loop Transfer Recovery (lqgltr)
Loop transfer recovery (LTR) is fully described in references [KS72,
DoS79,DoS81,SA88]. The properties of the recovery pertain to the LQG
feedback system as shown in Figure 4-8.
The parameter ρ (
rho) can be manipulated by the user to obtain loop
transfer recovery through the regulator (
lqrltr) or the estimator
(
lqeltr).