Practical controller design for discrete-valued input systems using feedback modulators

This paper deals with discrete-valued controller design for linear systems considering its input constraints on temporal and spatial resolutions. A feedback modulator (FBM) is introduced which converts continuous-valued control input to discrete-valued one, where the temporal resolution (i.e., switching rate of the input) is explicitly taken into account in continuous-time framework. Simply combining the FBM with a continuous-valued compensator appropriately designed in advance, a discrete-valued controller is constructed. First, an achievable tracking performance of such FBM-based control systems is given in the absence of the temporal resolution constraints. It turns out that the ultimate performance does not depend on the spatial resolution at all. Second, a simple design method of the feedback modulator is given based on the stability analysis considering the temporal resolution. This method does not require the precise knowledge of the system to control, and is quite easy to use. Effectiveness of the proposed method is demonstrated through numerical simulations, with comparison to conventional approaches such as PWM.