Digital Control Systems Hatem Elaydi Electrical Engineering Department Islamic University of Gaza Sep 6, 2015.

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Presentation transcript:

Digital Control Systems Hatem Elaydi Electrical Engineering Department Islamic University of Gaza Sep 6, 2015

Continuous vs. Discrete Time

Advantages Disadvantages Improved sensitivity Use software Control algorithms easily modified Many systems inherently digital Use the power of computer processing Develop complex math algorithms Lose information during conversions Needs interfacing

Digital Control Systems : Zero-Order Hold Digital Control Systems: Zero-Order Hold

Digital Control Systems : Zero-Order Hold (cont) Digital Control Systems: Zero-Order Hold (cont)

Digital Control Systems The z-transform Digital Control Systems: The z-transform Def’n of z-Transform: Relationship b/w s-plane and z-plane:

Digital Control Systems The z-transform (cont) Digital Control Systems: The z-transform (cont) Several common z-Transforms

Digital Control Systems : Stability in s-plane Digital Control Systems: Stability in s-plane Region of Stability: Left-Hand Plane

Digital Control Systems : Stability in z-plane Digital Control Systems: Stability in z-plane Region of Stability: Unit-Circle

Digital Control Systems : Root-Locus Digital Control Systems: Root-Locus

Digital Control Systems : Root-Locus (cont) Digital Control Systems: Root-Locus (cont)

Digital Control Systems : MATLAB to the rescue Digital Control Systems: MATLAB to the rescue c2d ◦ conversion of continuous-time models to discrete time zgrid ◦ generate z-plane grid lines for a root locus or pole- zero map over an existing map dstep ◦ Step response of discrete time system stairs ◦ Connects the elements from dstep to form stairstep graph

Digital Control Systems : Design Example Digital Control Systems: Design Example Root Locus Design for Digital DC Motor Position Control

Digital Control Systems : Design Example Digital Control Systems: Design Example