Equivalence of linear quadratic optimal design in the time domain and frequency domain for multivariable feedback systems

In this paper, the multivariable linear-quadratic optimal control is discussed. First, the LQR design of a model-following tracking system with load disturbance is considered. The equivalence of Wiener's design and the LQR design is then derived from the Laplace transform of the Riccati equation. A new concept, termed the generalized system description, is presented to aid the derivation of the equivalence and also to give a definition of the multivariable step (or ramp, etc.) input. Based on the equivalence, a procedure which combines the advantages of both the time-domain and frequency-domain approaches is suggested for the linear-quadratic optimal design of multivariable systems. A numerical example is given to illustrate the benefit of the presented results.