A challenging class of controlled pendulum (CP) type systems has been introduced in [I.A. Kunin, B. Kunin, Proc. 39th Annual Conf. Soc. Eng. Sci., Penn State University, University Park, PA, October 2002] in which examples have been computed using standard floating-point methods. This work deals with recently developed discrete methods [B.Yamrom, I.A. Kunin, G.A. Chernykh, Proc. 39th Annual Conf. Soc. Eng. Sci., Penn State University, University Park, PA, October 2002; I.A. Kunin, N. Shamsundar, R.W. Metcalfe, A Discrete Approach to Continuous Chaotic Systems, in preparation] applied to the same CP type systems in order to compare results using the two approaches and to address the issue of extracting additional information about the system that cannot readily be obtained using floating-point methods. These include such features as discrete cycles and transients leading to such cycles.