Active Vibration Control of Cantilever Beam using Multi-input Multi-output PPFR Controller

This paper presents a time-delay controller for vibration suppression of multi-input multi-output (MIMO) flexible structures with collocated piezoelectric actuator-sensor pairs. The proposed control design is the extension of a recently proposed controller, which is Positive Position Feedback controller with Retarded delay (PPFR). The controller is parametrized based on a mixed ℋ₂/ℋ_∞ optimization criterion which aims to improve both transient and steady-state performance of the controlled system. Genetic Algorithm (GA) is employed to solve the resulting nonconvex optimization problem due to nature of delay characteristics. Closed-loop stability is ensured by first verifying that the proposed controller is Negative Imaginary (NI), and then applying stability theorem for interconnection of (strictly) NI systems. Simulations on a truncated cantilever beam model with multiple sensor-actuator pairs demonstrate superior vibration suppression and reduced control effort compared to a benchmark controller.