Controlling Spatially Invariant Systems using Finite Arrays of Actuators and Sensors

Distributed parameter systems, where the underlying dynamics are spatially invariant, are common in a range of applications including the control of flows and smart structures or the cross-directional control of web processes. Bamieh et al. [1] have shown that controllers for these processes are also spatially invariant, leading to controller structures that are particularly simple to implement. However, these controllers use measurements that are continuous in space and generate control inputs that are are also spatially continuous. In practice, most applications use arrays of discrete, but identical actuators and sensors and this paper uses results from sampling theory to show that the controller can be implemented using these discrete arrays without loss of performance, provided that conditions on the separation between actuators and sensors are satisfied in order to avoid aliasing. It is shown that in many practical systems. Under these circumstances, it is better to incorporate the effect of aliasing by including the cross-coupling between aliased spatial frequencies in the system model.