Abstract
This paper describes two properties of the poles of the previously proposed optimal tracking systems1). The systems have no steadystate error for polynomial type inputs even if process parameter variations or constant disturbances exist.
One property concerns the asymptotic movement of the poles, as the weights on the inputs in the quadratic performance function go to zero. Though almost the same property was described by Kwakernaak2), the proof was not complete. This paper first proves that the degrees of the coefficients in the power characteristic equation are inherent in a process and have a monotonic nature. Using those theorems, complete proof states that those poles that go to infinity group into m Butterworth pole configurations of the inherent orders of the process. Here, m is the number of inputs and outputs. The number was not explained in Kwakernaak's paper.
The other property is that the product of the absolute values of the poles is in proportion to the product of the determinants of the weighting matrices in the function.
These properties are expected to be useful to determine the specific values of the weighting matrices. An example demonstrate the above mentioned properties.
