Reference input -II 16. 3117-23 On page 17-5, compensator implemented with a reference command y changing to feedback on e(t=r(t-y(t) rather than -y(t)

Weighting Matrix Selection a good rule of thumb when selecting the weighting matrices Rxx (or Ru and R uu is to normalize

Deterministic lOR Optimal control and the riccati equation · Lagrange multipliers The Hamiltonian matrix and the symmetric root locus Factoids: for symmtric R

Bounded gain There exist very easy ways of testing(analytically) whether S Gu)< SISO Bounded Gain Theorem: Gain of generic stable system

Model Uncertain Prior analysis assumed a perfect model. What if the model is in correct= actual system dynamics GA(s)are in one of the sets Multiplicative model G,(s=GN(s(1+E(s)) Additive model Gp(S)=GN(S)+E(s) where

MIMO Systems Singular Value Decomposition Multivariable Frequency Response Plots Copyright 2001 by Jonathan How

tate-Space Systems Closed-loop control using estimators and regulators Dynamics output feedback “ Back to reality' Copyright[2001by JOnathan dHow

Closed-loop system analysis Robustness State-space -eigenvalue analysis Frequency domain- Nyquist theorem Sensitivity Copyright 2001 by Jonathan How

State-Space Systems e Ful-state feedback Control How do we change the poles of the state-space system? Or, even if we can change the pole locations Where do we change the pole locations to? How well does this approach work?

State-Space Systems Open-loop Estimators Closed-loop Estimators Observer Theory (no noise)-Luenberger IEEE TAC Vol 16, No. 6, pp. 596-602, December 1971 Estimation Theory(with noise)-Kalman Copyright [2001 by JOnathan dHow