Extension of analytical design techniques to multivariable feedback control systems

Analytical design techniques are developed for multivariable feedback control systems. The design includes a saturation constraint and provides for a disturbance at the system output and additive noise at the system input. The system inputs (signal, noise, and disturbance) are assumed to be generated by independent, stationary, stochastic processes that are adequately represented by rational power-spectral-density matrices. System elements are represented by rational transfer function matrices using the bilateral Laplace transform. The design is applicable to linear time-invariant systems. Design formulas are derived for the general case where the transfer function matrix representing the fixed elements of the system may not be square. The basic design consists of minimizing a weighted sum of the output mean-square errors and the mean-square values of a selected set of saturation signals. A variational technique is used in the optimization, and the technique of spectral factorization is used to obtain a solution. An example is presented to illustrate the design procedure.