Flexible structures are continuum modelled as infinite degrees of freedom. The finite element methods are used with a finite number of degrees of freedom to analyze these structures. The analysis and control of the dynamics of these structures need simulations of a large degree of freedom in real-time. This is computationally expensive. The current study focuses on developing a reduced-order framework for dynamics and control of flexible structures, with beam as an example. Essentially, in the proposed framework, full order state-space obtained from finite element modelling of the flexible structure has been reduced to a lower subspace using a reduced order algorithm, keeping the key dynamical characteristic intact. The transformation matrix for reduction has been developed using the system equivalent reduction expansion process (SEREP).

The beam considered is integrated with multiple piezoelectric sensors and actuators. A finite element model is created for the complete system. Full order dynamical system is used to find a gain matrix to suppress the uncontrolled dynamics associated with the system. Thereafter, the reduced dimension of state space of the system is used for estimating the gain matrix. The gain obtained through the reduced system is subsequently used as feedback to the attached actuators which then produce the required force to control the system. The numerical example of the flexible cantilever beam has shown the effectiveness of the algorithm. The method is then extended to beams with uncertain parameters. A linear control algorithm is used to control the beam.