Practical design of multirate output controllers

Multirate output controllers (MROC) sample plant outputs at a faster rate than they change plant inputs. Consequently, they offer greater flexibility for control design than conventional single-rate controllers do. This paper describes a method for practical design of MROC. The first contribution is the development of a time-invariant discrete-time model for the closed-loop that captures the intersample behavior. Next, conditions under which an MROC design is equivalent to the synthesis of a full-information controller (i.e., one for which state and disturbance input are available for feedback) are derived; the latter problem is solved by standard techniques. The MROC gains determined through this approach, while being theoretically optimal, are very large in magnitude and exhibit very poor noise sensitivity. We address this issue by posing a practical MROC design problem where the objective is to minimize the effect of measurement noise on performance, subject to closed-loop poles being in a region of the complex plane. We present a procedure for decreasing controller gains, and demonstrate its performance on a numerical example.