Fixed-point digital controller

After system modeling, controller synthesis and closed-loop simulation, the control engineer has still to implement the controller. In many applications, the controller must be realized with a fixed-point digital processor. The translation of the synthesized controller to its fixed-point realization is intrinsically difficult, because there are an infinite number of solutions and the optimum criterion is not well defined. One would like a fixed-point controller to require as little as possible computing power while at the same time to be the closest from the ideal controller, i.e., the synthesized controller. If it is difficult to define and reach the optimal controller, it is already not obvious to find a sub-optimal but working fixed-point controller. This work presents the key points that allow a computer to automatically derive a fixed-point realization of any given discrete-time transfer function. The derivation can be controlled by three parameters, one being the number of initial derivative, another the number of initial delay and the last one the number of bits of the processor words. An increase of any of these three parameters enhances the quality of the realization for a relatively small extra cost of computing power.