Abstract
This paper proposes a new method to design linear multi-input-output optimal tracking systems. The systems have no steady-state error for polynomial type inputs even if process parameter variations or constant disturbances exist. This characteristic is obtained by introducing the structure with an integral control action over an error to the systems.
The design procedure is divided into two steps. In the first step, the original systems are augmented with a necessary number of integrators in cascade with each input line. Then the augmented systems are regarded as “processes” to be designed. An ordinary optimal regulator problem is formulated for the “processes” and solved. In the second step, the above augmented optimal regulator systems are transformed to have the above mentioned structure, maintaining the transfer functions matrices unchanged.
The other characteristics of the systems are as follows.
(1) The systems preserve all the characteristics of the optimal regulator systems.
(2) The control inputs have no discontinuity even at the time origin.
(3) No such input derivative is necessary, even in the case of polynomial type inputs, as other systems require5), 7).
Necessary and sufficient conditions are also derived to synthesize the control systems. Some examples demonstrated the above mentioned characteristics.
