Vibratory disturbances degrade the performance of a system in many ground and space based applications. A passive mechanical isolator or active isolation system is incorporated to attenuate these unwanted vibrations. An active isolation system comprises a passive mechanical isolator, sensors, actuators, and generally a digital controller. Such an approach to attenuate vibration is generally referred to as active vibration control (AVC). Several digital controllers have been proposed in the area of AVC such as Proportional-Integral-Derivative(PID), Linear Quadratic Regualtor(LQR)/Linear Quadratic Gaussian(LQG), H-infinity,etc. These controllers have an inherent drawback either in handling actuator constraints, modelling errors or optimality. Model Predictive Control (MPC) is one such controller that can handle all these systematically but with computational overhead. With the advent of a faster computing system and the development of faster optimisation algorithms, MPC is slowly being adopted in the area of active vibration control which comprises both low and high-frequency dynamics. An active vibration control (AVC) using MPC for controlling the free vibration of a smart flexible system is referred to here as an AVMPC. When compared to an optimal controller LQR, AVMPC is a sub-optimal control because of its finite horizon in its prediction. Within the framework of MPC and solving the infinite horizon control problem, an Active Vibration Dual-mode MPC (AVDMPC) is proposed. In AVDMPC, switching between modes does not happen in real-time, but rather is a description of how the predictions are set.

In this research work, a flexible beam with collocated piezo sensors and actuators is used as a smart flexible system (SFS). The mathematical model (prediction model) of a smart flexible system required for implementing MPC is obtained through the Finite Element Method-State Space (FEM-SS) approach. The accuracy of the reduced order mathematical model of SFS obtained through FEM-SS approach is compared with that of experimental results. The controller bandwidth is set up to 200 Hz and input constraint is set to 100V. For a fair comparison, the performance of AVDMPC is compared with the other two controllers (AVMPC and LQG) for SSCE (Sum Squared Control Error), control effort, and percentage of vibration attenuation achieved.

The outcome of the research shows that 1) The AVDMPC is capable of attenuating free vibrations of the SFS for its first two resonant modes of 30 Hz and 160 Hz to 50\% and 95\% respectively. 2) In an unconstrained case , for the same prediction horizon set in AVMPC and AVDMPC, there is an enhancement of 30\% attenuation capability in AVDMPC at higher controller bandwidth. 3) In a constrained case, AVDMPC do not violate the input constraint for the entire control bandwidth for the tuned parameters set at lower control bandwidth compared to LQG controller.