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# topic19 - Topic#19 16.31 Feedback Control Systems •...

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Unformatted text preview: Topic #19 16.31 Feedback Control Systems • Stengel Chapter 6 • Question: how well do the large gain and phase margins discussed for LQR map over to DOFB using LQR and LQE (called LQG)? Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Fall 2007 16.31 19–1 Linear Quadratic Gaussian (LQG) • When we use the combination of an optimal estimator and an op- timal regulator to design the controller, the compensator is called Linear Quadratic Gaussian (LQG) – Special case of the controllers that can be designed using the separation principle. • Great news about an LQG design is that stability of the closed-loop system is guaranteed . – The designer is freed from having to perform any detailed me- chanics- the entire process is fast and automated. – Designer can focus on the “performance” related issues, being confident that the LQG design will produce a controller that stabilizes the system. Selecting values of R zz , R uu and relative sizes of R ww & R vv • This sounds great – so what is the catch?? • Remaining issue is that sometimes the controllers designed using these state space tools are very sensitive to errors in the knowledge of the model. – i.e., the compensator might work very well if the plant gain α = 1 , but be unstable if α = 0 . 9 or α = 1 . 1 . – LQG is also prone to plant–pole/compensator–zero cancelation, which tends to be sensitive to modeling errors. • J. Doyle, ”Guaranteed Margins for LQG Regulators”, IEEE Trans- actions on Automatic Control , Vol. 23, No. 4, pp. 756-757, 1978. November 18, 2007 Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Fall 2007 16.31 19–3 • The good news is that the state-space techniques will give you a controller very easily. – You should use the time saved to verify that the one you designed is a “ good ” controller. • There are, of course, different definitions of what makes a con- troller good , but one important criterion is whether there is a reasonable chance that it would work on the real system as well as it does in Matlab. Robustness . ⇒ – The controller must be able to tolerate some modeling error, because our models in Matlab are typically inaccurate....
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## This note was uploaded on 11/07/2011 for the course AERO 16.31 taught by Professor Jonathanhow during the Fall '07 term at MIT.

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topic19 - Topic#19 16.31 Feedback Control Systems •...

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