MS COMPREHENSIVE / PH.D. QUALIFYING EXAM AUTOMATIC CONTROL TOPICS

Laplace, Z transforms: basic properties, use in solving linear differential/difference equations, application to system analysis, transfer functions. Fourier transform, Fourier series: basic properties, application to signal analysis, frequency response, spectral energy density. B. Basic Concepts Linearity, time invariance, causality, difference and differential systems, linearization, signal-flow and block diagrams, BIBO and asymptotic stability. C. Classical Control Transient and steady state analysis and performance indicators, pole location, sensitivity; frequency domain analysis, phase and gain margins; Nyquist stability, Routh-Hourwitz criterion, root locus, lead and lag compensator design, PID control; pole placement with fractional controllers. D. Sampled Data Systems Basic A/D and D/A conversion, sampling theorem. continuous time systems, deadbeat control. Discretization of E. State Space Control for Continuous and Discrete Time Systems State and state equations, transition matrix, solution of state equation. Realization, controllability and stabilizability, observability and detectability, Lyapunov stability, state feedback and pole placement, asymptotic observers, state feedback with observers