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MIT16_30F10_lec19

MIT16_30F10_lec19 - Topic#19 16.31 Feedback Control Systems...

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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)?
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Fall 2010 16.30/31 19–2 Linear Quadratic Gaussian (LQG) When we use the combination of an optimal estimator (not discussed in this course) and an optimal regulator to design the controller, the compensator is called Linear Quadratic Gaussian (LQG) Special case of the controllers that can be designed using the sep- aration 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 mechanics - the entire process is fast and automated. Designer can focus on the “performance” related issues, being con- fident 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 Transac- tions on Automatic Control , Vol. 23, No. 4, pp. 756-757, 1978. November 5, 2010
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Fall 2010 16.30/31 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.
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