Review for Exam 1 – Fall 2008 Modern Control Potential Topics on Exam 1: 1. State-space representation (SSR): state vector, control vector, output vector, and matrices A , B , C , and D . 2. Linearization: 1) select reference pt (equilibrium or operating point) and define perturbation variables w.r.t. reference, 2) sub for states and controls in terms of reference states/controls and perturbation states/controls; 3) expand nonlinear equations in Taylor series about reference states/controls and keep only first-order terms. 3. Canonical forms: CCF 4. Eigenvalues: det( λ I – A ) = 0. System (free) response is based on eigenvalue locations in the complex plane (damping ratio, undamped natural frequency, damped frequency, etc). 5. State transformations: z = P x (eigenvalues remain unchanged) 6. Solution to the state equation: natural (“free”) + forced responses 7. State transition matrix (STM) and how to obtain the STM: 1) series solution, 2) Laplace transform method, 3) direct numerical integration, 4) diagonalization. 8.
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 01/12/2011 for the course MAE 4720 taught by Professor Dr.kluever during the Spring '10 term at Missouri (Mizzou).