Optimal Placement of Actuators in the Precision Control of Truss Structures

Abstract

Actuator placement criteria in truss structures are based on satisfying two goals: (1) precision control (displacement control) of precision points, and, (2) prestressing control (i.e., creation of initial stresses) to counteract joint looseness. It is shown that stress-free exact displacement control is possible in (a) statically determinate trusses using as many actuators (q) as the number of independent degrees of freedom at precision points (p), i.e., q = p; (b) in statically indeterminate trusses using q = p + r actuators, where r is the degree of redundancy. Using (a) q < p actuators in statically determinate trusses will allow only for approximate displacement control, and, (b) using q < p+r actuators, in statically indeterminate trusses, will allow for: (1) exact, stress-induced displacement control if q > p, with q-p actuators to relieve stress as best as possible; (2) approximate, stress-free displacement control if p > q > r, or, (3) approximate, stress-induced displacement control if q < p and q < r. For prestressing control using actuators, the structure must be indeterminate at least to degree 1. If indeterminate to degree r, it is either possible to (a) exactly control a maximum of r components of member forces (using q = r actuators), or, (b) exactly control all member forces, provided they lie in the column space of the null matrix of the coefficient matrix of bar forces in the force equilibrium equations of the joints (using q = r actuators). By using q < r actuators, it is possible to exactly control only q components of member forces. It is also shown that, with sufficient number of actuators, prestressing control with no disturbance to precision points is possible. Optimal actuator placement schemes are studied for some of the above cases of precision control and prestressing control, based on objectives which are specific to each case. In statically indeterminate truss structures the optimal placement criteria and techniques differ depending on whether the primary determinate structure is known or not. A suboptimal actuator placement solution to the global optimization problem, combining the objectives of displacement control and prestressing control, is suggested (for the case q < p and q < r) by combining the results of the separate optimization problems (displacement control, prestressing control); the suboptimal solution is improved (with respect to global optimum) by iteration.