topic24 - Topic #24 16.31 Feedback Control Systems H...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Topic #24 16.31 Feedback Control Systems H Synthesis SP Skogestad and Postlethwaite(1996) Multivariable Feedback Control Wiley. JB Burl (2000). Linear Optimal Control Addison-Wesley. ZDG Zhou, Doyle, and Glover (1996). Robust and Optimal Control Prentice Hall. MAC Maciejowski (1989) Multivariable Feedback Design Addison Wesley. 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 16.31 241 Synthesis For the synthesis problem, typically define a generalized version of the system dynamics (SISO or MIMO) P zw ( s ) P zu ( s ) P yw ( s ) P yu ( s ) G c w u z y Signals: z Performance output w Disturbance/ref inputs y Sensor outputs u Actuator inputs Generalized plant: P ( s ) = P zw ( s ) P zu ( s ) P yw ( s ) P yu ( s ) contains plant G ( s ) and all perfor- mance/uncertainty weights With the loop closed ( u = G c y ), can show that z = P zw + P zu G c ( I P yu G c ) 1 P yw w F l ( P, G c ) w Called a (lower) Linear Fractional Transformation (LFT). Define the H norm for a TFM P ( s ) as P ( s ) = sup [ P ( j )] Basically finds the peak amplification possible for the TFM over all frequencies (works for MIMO). December 9, 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 16.31 242 Design Objective: Find G c ( s ) to stabilize the closed-loop sys- tem and minimize F l ( P, G c ) . Hard problem to solve, so typically consider suboptimal problem: Find G c ( s ) to satisfy F l ( P, G c ) < Then use bisection (called a iteration ) to find the smallest value ( opt ) for which F l ( P, G c ) < opt hopefully get that G c approaches G opt c Consider the suboptimal H synthesis problem: 1 Find G c ( s ) to satisfy F l ( P, G c ) < P ( s ) = P zw ( s ) P zu ( s ) P yw ( s ) P yu ( s ) := A B w B u C z D zu C y D yw where it is assumed that: 1. ( A, B u , C y ) is stabilizable/detectable (essential) 2. ( A, B w , C z ) is stabilizable/detectable (essential) 3. D T zu [ C z D zu ] = [ 0 I ] (simplify/essential) 4. B w D yw D T yw = I (simplify/essential) 1 SP367 December 9, 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 16.31 243 There exists a stabilizing G c ( s ) such that F l ( P, G c ) < iff (1) X that solves the ARE A T X + XA + C T z C z + X ( 2 B w B T w B u B T u ) X = 0 and R i A + ( 2 B w B T w B u B T u ) X < i (2) Y that solves the ARE AY + Y A T + B T w B w + Y (...
View Full Document

Page1 / 12

topic24 - Topic #24 16.31 Feedback Control Systems H...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online