The Role of Internal Variables on the Control of Viscoelastic Structures

Scientists have used internal variables to model time-dependent material behavior for many years. Since the 1980s they have been employed to predict transient response of structures that include viscoelastic materials. The potentially large number of extra states introduced by the internal variables can be problematic when designing control systems, so the purpose of this paper is to explore how internal variables affect control system design. Practical designs are based on output feedback of a limited number of the physical states, but this brings up the question of whether it is advantageous to recreate the full state vector (including internal states) using a standard observer. Internal variables based on Maxwell models are used to address observability and controllability as well as full- and partial-state feedback on a single-degree-of-freedom system. Comparisons are also made between complex-modulus and internal-variable representations of viscoelastic behavior.