Statistical design of linear discrete-data control systems via the modified z-transform method

Abstract A solution is presented for the analytical design of digital controller in accordance with a specified optimum criterion. This approach makes use of the modified z -transform technique. The analytical design procedure for systems with random noise occurring in the input channel and for those with random noise occurring at a point in the control loop is developed via modified z-transformation. Much attention is centered upon stationary random functions because of their frequent occurrence in control systems and their being amenable to mathematical treatment. In this paper, physical realizability and system constraints are considered, general design equations for both cases of noise occurrence are derived, and systems with deterministic inputs are discussed.

[1]  R. M. Stewart.  Statistical Design and Evaluation of Filters for the Restoration of Sampled Data , 1956, Proceedings of the IRE.

[2]  K. D. Tocher,et al.  Sampled‐Data Control Systems , 1959 .

[3]  T. Julius Tou,et al.  Optimum control of nonlinear discrete-data systems , 1961, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[4]  R. Kálmán,et al.  A unified approach to the theory of sampling systems , 1959 .

[5]  R. H. Barker,et al.  The pulse transfer function and its application to sampling servo systems , 1952 .

[6]  J. Tou,et al.  Statistical design of digital control systems , 1960 .

[7]  Edward O. Gilbert.  A method for the symbolic representation and analysis of linear periodic feedback systems , 1960, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[8]  S. Chang,et al.  Statistical design theory for digital-controlled continuous systems , 1958, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[9]  L. A. Zadeh,et al.  The analysis of sampled-data systems , 1952, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[10]  Julius T. Tou,et al.  Digital and sampled-data control systems , 1963 .