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The dynamic properties of vibration control systems pose unique requirements and challenges on the implementation of model predictive control (MPC) algorithms with stability and feasibility guarantees. This article presents a comprehensive experimental comparison of computation timing and damping performance for various MPC methods; analyzing their offline and online properties in active vibration control and their impact on practical implementability. Optimal and sub-optimal MPC algorithms providing guaranteed stability and constraint feasibility have been applied to the real-time active vibration attenuation of a lightly damped mechanical test structure. Based on the experiments presented in this paper, the standard and sequential quadratic programming-based, optimal and sub-optimal minimum time multi-parametric programming-based and the sub-optimal Newton–Raphson’s algorithm-based MPC methods demonstrate closely comparable vibration attenuation performance. The offline and online timing analysis indicates that the underlying difference between the investigated MPC algorithms lies mainly in practical implementability difficulties caused by inherent algorithm efficiency, rendering certain variants of MPC more suitable for vibration control than others.

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This paper presents an adaptive-predictive vibration control system using extended Kalman filtering for the joint estimation of system states and model parameters. A fixed-free cantilever beam equipped with piezoceramic actuators serves as a test platform to validate the proposed control strategy. Deflection readings taken at the end of the beam have been used to reconstruct the position and velocity information for a second-order state-space model. In addition to the states, the dynamic system has been augmented by the unknown model parameters: stiffness, damping constant, and a voltage/force conversion constant, characterizing the actuating effect of the piezoceramic transducers. The states and parameters of this augmented system have been estimated in real time, using the hybrid extended Kalman filter. The estimated model parameters have been applied to define the continuous state-space model of the vibrating system, which in turn is discretized for the predictive controller. The model predictive control algorithm generates state predictions and dual-mode quadratic cost prediction matrices based on the updated discrete state-space models. The resulting cost function is then minimized using quadratic programming to find the sequence of optimal but constrained control inputs. The proposed active vibration control system is implemented and evaluated experimentally to investigate the viability of the control method.

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This paper presents a structural health monitoring and parameter estimation system for vibrating active cantilever beams using low-cost embedded computing hardware. The actuator input and the measured position are used in an augmented nonlinear model to observe the dynamic states and parameters of the beam by the continuous-discrete extended Kalman filter (EKF). The presence of undesirable structural change is detected by variations of the first resonance estimate computed from the observed equivalent mass, stiffness, damping, and voltage-force conversion coefficients. A fault signal is generated upon its departure from a predetermined nominal tolerance band. The algorithm is implemented using automatically generated and deployed machine code on an electronics prototyping platform, featuring an economically feasible 8-bit microcontroller unit (MCU). The validation experiments demonstrate the viability of the proposed system to detect sudden or gradual mechanical changes in real-time, while the functionality on low-cost miniaturized hardware suggests a strong potential for mass-production and structural integration. The modest computing power of the microcontroller and automated code generation designates the proposed system only for very flexible structures, with a first dominant resonant frequency under 4 Hz; however, a code-optimized version certainly allows much stiffer structures or more complicated models on the same hardware.