Jawaharlal Nehru Technological University Hyderabad B.Tech IV Year DIGITAL CONTROL SYSTEMS Previous Question Paper (January/February - 2023 - R18)

Sampling is the process of converting a continuous-time signal into a discrete-time signal by taking periodic measurements of the signal's amplitude at fixed intervals of time, denoted by the sampling period T. This process effectively discretizes the time axis, allowing a continuous system to be processed by a digital computer or controller.

Discrete-time systems are characterized by the following key features:

• Sampling: The system operates on signals that are defined only at discrete time intervals, typically represented as a sequence of numbers x(kT), where T is the sampling period.
• Difference Equations: Unlike continuous systems described by differential equations, discrete-time systems are modeled using linear constant-coefficient difference equations, which relate the current output to past inputs and past outputs.
• Z-Transform Analysis: The behavior and stability of these systems are primarily analyzed using the Z-transform, which serves as the discrete-time equivalent of the Laplace transform, mapping the system from the time domain to the complex z-domain.
• Digital Implementation: These systems are inherently suitable for implementation on digital computers or microprocessors, allowing for flexible control algorithms that can be easily updated via software.