Error analysis of discrete-time models without a direct term for Band-Limited measurements

Most real systems and processes are continuous in nature but most of the control strategies are implemented using a digital computers. Therefore a discrete-time representation of the continuous-time system under consideration is required in order to achieve a good performance in control as well as simulation. These discrete-time representation of the continuous time system can be developed under a zero-order hold (ZOH) or Band-limited assumption of the inter-sample behavior [7]. It is important to quantify the relative error of the approximate discrete-time models. In this paper, we analyze the additional error that is introduced by forcing the direct term of the discrete-time model equal to zero for the Band-limited measurements. Such models are more convenient when used to simulate nonlinear feedback systems. The presence of a delay removes the nonlinear algebraic loops so that simple recursive simulation becomes possible. In this work, we present for a special case, where both the generator and system are a first order continuous-time systems with same time constant i.e fgen = fsys = fB, an analysis of relative error of the discrete-time model with respect to the bandwidth and the sampling frequency under the Band-limited assumption. This analysis is important because the design of an identification experiment based on Band-Limited assumption is often more realistic, easier and appropriate to realize during identification of a complex nonlinear system as compared to the zero-order hold (ZOH) assumption.