Robust multiobjective controllers for smart structures

Flexible smart structures are large mechanical structures with applications in which specific performance characteristics are desired in the presence of parameter variations and disturbances. These structures tend to have severe controller effort restrictions and tightly spaced lightly damped modes. When designing controllers for smart structures, H₂ controllers are well suited for control effort restrictions and closed loop performance specifications while H_∝ controllers are better suited for modeling uncertainties. This paper examines the application of H₂/H_∞ controller design methodologies to smart structures. A unique feature of mechanical distributed systems is that state space systems can be determined from finite element models (FEM) in which the states have physical significance. For certain systems, these states can be directly measured by using a distributed PVDF film appropriately shaped and applied to the structure. This full state feedback system allows for the implementation of H₂/H_∞ full state feedback algorithms. The development of a control system implementing this type of algorithm is described for a simple cantilever beam. In addition, a H₂/H_∝ algorithm developed by Bernstein and Haddad is investigated for the cantilever beam. This method does not require state measurement, but the controller design algorithm is slightly more complicated. This algorithm requires the solution of one algebraic Riccati equation and two coupled algebraic Riccati equations which are solved iteratively.