Abstract
An approximate pole assignment procedure is proposed for some class of first order partial differential equation system whose transfer function has no bounded poles but bounded poles appear when it is feedback controlled.
As this system is equivalent to a system with delay in control, the finite spectrum assignment procedure by A. Manitius et al. seems to be applicable. However it can not be used for this system, since the equivalent system is found not to be absolute controllable.
The original distributed parameter system is approximated by applying the method of weighted residuals. When a feedback control law derived from the approximate system is applied to the original distributed parameter system, the resulting poles are apt to run into unstable region though the locations of assigned poles are in sufficiently stable region. It is found that this instability can be avoided when the two conjugate poles of the approximate system having the largest imaginary parts are fixed in the original locations and the residual approximate poles are appropriately assigned. Moreover, good pole assignments is obtained when the residual poles are assigned in the right hand side of the pole locations of the approximate system.
