DISCRETE CONTROL SYSTEMS

The course studies control strategies and their implementation in the discrete domain. Introduction with examples; review of continuous control and Laplace Transforms; review of continuous state-space representation and Solutions; review of  difference equations, discretization in time and frequency, the WKS (aka Shannon) sampling theorem, windowing, filters, Transforms: Fourier series, Fourier transform, z-transform and their inverses; Ideal sampler, Sample-and-hold devices, zero, one, polygonal, and slewer hold; Transfer functions, block diagrams, and signal flow graphs for discrete systems; Discrete State-Space transformation, controllabililty, observability, and stability in the state-space domain. Discrete time and z domain analysis, steady state analysis, discrete-time root-locus, and pole-zero placement; Discrete Nyquist stability criterion, Bode plot, Gain and Phase Margin analysis, Nichols chart, bandwidth and sensitivity analysis; Design criteria, self-tuning regulator, Kalman filter, and simulation, followed by advanced stability analysis such as Lyapunov stability; Overview of the discrete Euler-Lagrange equations, discrete maximum and minimum principle, optimal linear discrete regulator design, optimality and dynamic programming.