Modern analytical design of optimal multivariable control systems

A least square Wiener-Hopf technique and its use to develop an optimum multivariable controller are discussed. The resulting system is, (1) dynamical and minimizes the cost functional, (2) guarantees a dynamical asymptotically stable closed-loop design with an acceptable sensitivity matrix, (3) enables the loop to follow generalized polynomial modulated sinusoidal type inputs of the correct order and to recover from step-type load disturbances with zero steady-state error, (4) permits a tradeoff between transient response and rms saturation level to be achieved by an appropriate choice of positive constant, (5) incorporates feedforward compensation and measurement noise directly into the cost and, (6) encompasses improper, unstable, nonminimum-phase and rectangular plants. Above all, the stability margin of the optimal design can be ascertained in advance. The physical assumptions underlying the choice of model are discussed in depth.