Reducing bandwidth usage for controlling systems with many actuators

The advent of digital networks has considerably simpli ed the design and management of complex control systems, by reducing the need for dedicated communication lines between computers, actuators, and sensors. Instead, all actuators and sensors are part of the same communication line. They can be individually addressed through the assignment of unique identi ers. Such communication architectures are commonplace in modern commercial and military aviation, for which speci c communication standards, such as Mil-Std1553 or ARINC 429, have been established. They are also standard in automobiles, with the wide usage of the CAN digital communication bus. In this paper, we are interested in control systems where a large number of smart, networked actuators are present. For high-bandwidth applications, such as segmented telescopes and exible aero-elastic wings, addressing actuator individually may not be possible due to communication bandwidth limits. Previous approaches for designing computer-controlled systems with large numbers of actuators include Yook and Tilbury. Likewise, Lin and Crawley were concerned with the distributed control of an aeroelastic wing with many piezo-electric actuators. The authors proposed that actuators be grouped into a few ’superactuators’ based on openand closed-loop controllability metrics to reduce the number of communication links from the control computer to the actuators. Minor extensions of Crawley and Lin’s work have been proposed since. In a recent paper, Winck and Book consider a related problem controlling digital clay. Due to speci c mechanical constraints, collective addressing of speci c groups of clay elements are shown to be much more preferrable to individual clay element addressing, a point that motivated the present study. This note builds upon that of Lin and Crawley, by leveraging the advances in digital networking technologies that have happened since their work was published. Although very di erent from the topic addressed in this paper, the work of Winck and Book also constitutes a core inspiration for the work presented here. In our approach, the vector space of control inputs is analyzed to identify the low-dimensional, ’control subspace’ spanned by the closed-loop control activity. Next, ’virtual actuators’, are designed to approximately span the entire control subspace. Typically, the number of virtual actuators is much smaller than the original set of actuators, resulting in signi cant communication bandwidth reduction. Unlike the architecture proposed by Lin and Crawley, the same physical actuator can contribute to more than one virtual actuator. The rest of this paper is organized as follows. First, we formally introduce the linear system to be controlled, and we state the tracking problem to be solved. We then introduce full-state and output feedback controllers that solve the tracking problem. For both controllers, we describe a procedure to build virtual actuators. We then illustrate our approach by means of a numerical example, and we discuss the implementation of the virtual actuators in reduced-bandwidth communication architectures.