Discretizing of linear systems with time-delay Using method of Euler’s and Tustin’s approximations

Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime\ud signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control\ud applications, the data as seen from the computer and systems involved are naturally discrete-time because a\ud computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems\ud is useful in design and analysis of control systems, signal filters, state estimators and model estimation from\ud time-series of process data system identification. In this paper, a new approximated discretization method and\ud digital design for control systems with delays is proposed. System is transformed to a discrete-time model with\ud time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model\ud type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most\ud important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended\ud discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed\ud control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate\ud the effectiveness of the developed method