A systematic design method is proposed for
the selecting of actuators and sensors in the structural control
in order to minimize the instrumental cost. With actuators and
sensors placed at all the admissible locations initially, an
iterative minimization algorithm is carried out to identify the
sensor/actuator that requires the least precision. By deleting the
roughest sensor/actuator each time till loss of feasibility, one
can conclude simultaneously the necessary number and type of
sensor/actuator, and the location and precision for each
sensor/actuator. A tensegrity structure example has
been solved as an application of the proposed algorithm.
The economic simulation design problem is that given performance requirements, design the simulation of a linear system and distribute precision among the instruments such that the computational cost is minimized without violating the simulation accuracy. In this paper, we consider the simulation of a large-scale linear system in digital devices with fixed-point arithmetic and finite wordlength. Given the output variance upperbound, we focus on finding an optimal realization and the allocation of wordlength among A/D converter, computer and sensors. This problem is in general not convex because of the scaling constraint. By exploring the special structure of this
joint optimization problem and under reasonable assumptions, we simplify this problem and find the optimal coordinate transformation and the wordlength allocation scheme simultaneously by solving LMIs (linear matrix inequalities). Numerical results are given which compare this new realization with the balanced realization and random realizations.