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Many industrial systems can be represented by a linear multivariable system with time-delays in inputs. In this paper an optimal control problem of such a system is discussed when the reference inputs are polynomial functions of time. The outline of the synthesis is as follows: A new tracking error is defined, where inevitable error due to the system's time delays is not evaluated. The integrated value of the tracking error is also introduced in order to incorporate integral-type controllers into the control system. By imbedding the delayed inputs into the system's state variables, the equation of the controlled system is transformed to a usual state equation without time-delays. A criterion function is a quadratic form of the tracking error, its integrated value and the deviation of controls from their steady state values which are determined so that the system's outputs coincide with the reference inputs. By using this criterion function the synthesis problem is reduced to a standard regulator problem which is easily solved. Advantages of this method are as follows: (1) The optimal control law can be easily derived. (2) The control system has feedback, feedforward and predictive control pass. (3) Offsets due to system parameter variations or disturbances never arise, because the integral-type controllers are incorporated in the control system. (4) Even if the controlled system's time-delays are large, the integral-type controllers do not deteriorate transient characteristics of the control system, because the integral actions are delayed as much as the system's time delays. (5) The parameters of the control system depend only on the parameters of the controlled system and on the weighting matrices of the criterion function, and are independent of the reference inputs. 1. ま え が き

Synthesis of Digital Feedforward-Feedback Control System for Multivariable System with Inputs Delays