On properties and applications of a new form of discrete time optimal control law

Unlike the well-known bang-bang control for continuous plants, the closed-form time optimal control for discrete time plants was obtained only recently (Z. Gao, 2004, J. Han, 1999). It is shown in this paper that this new discrete time optimal control (DTOC) law offers a practical alternative to bang-bang control. A particularly interesting property of DTOC is that the control signal is not always bang-bang. Instead of constant chattering, DTOC can produce a smooth control signal that results in a similar performance to that of the bang-bang control. Helpful insight is offered on how to maintain the smoothness of control signal in the presence of significant sensor noises. Superior robustness of the new control law is demonstrated for a general second order system with substantial dynamic uncertainties. Implementation issues and the tuning of the control parameters are also discussed. Finally, the performance of the new control law is examined in an industrial motion control case study and a computer hard disk drive problem.