OPTIMAL CONTROLLERS FOR FINITE WORD-LENGTH IMPLEMENTATION

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exist realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Therefore, it is important to have a systematic way of reducing these effects. With the assumption of sufficient excitation of the system, this paper solves the problem of designing an optimal controller in the presence of both external disturbances and internal round-off errors from the control computer and the D/A and A/D converters. These results provide a natural extension to the LQG theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision, the separation principle does not hold. A penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller. This minimum sum can be used to represent the lower bound on computer memory needed for controller synthesis. This is one measure of controller complexity, and this measure is minimized (penalized) in this paper.