Abstract
In the design of digital control systems, the time delay due to computation time of a processor cannot be often neglected. In this paper, we consider the problem of synthesizing a type-1 optimal digital servosystem taking account of controller delay of one sampling period.It is first shown that the optimal digital servo problem in which a quadratic criterion function is defined for a given continuous-time plant can be reasonably reformulated to a discrete optimal regulator problem. To assure the solvability of this problem, some conditions for the preservation of stabilizability and detectability of the plant under sampling are given. In the discrete optimal regulator problem considered here, not only control input but also the initial state of the servocompensator are referred as free design parameters. The obtained optimal digital control law contains a feedforward term of reference signal in addition to a feedback term. It is also shown that the optimal control law has a function of estimating the state variables at the following sampling period in order to recover the controller delay.
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