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

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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 16.31 191 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 = 1 , but be unstable if = 0 . 9 or = 1 . 1 . LQG is also prone to plantpole/compensatorzero 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 16.31 193 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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topic19 - Topic #19 16.31 Feedback Control Systems Stengel...

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