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.
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state transition matrix, test matrix, Optimal gain matrix, T-transformation matrix method