Adaptive Model Predictive Vibration Control of a Cantilever Beam with Real-Time Parameter Estimation

Gergely Takács,Tomáš Polóni,Boris Rohal’-Ilkiv

doi:10.1155/2014/741765

Gergely Takács, Tomáš Polóni + Show 1 more

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https://doi.org/10.1155/2014/741765

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Abstract

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.

Highlights

Undesirable mechanical and structural vibrations may often cause discomfort in humans and in certain engineering applications can even lead to catastrophic failure or other extreme consequences
This assumption enables the straightforward tuning of some controllers used in vibration attenuation like positive position feedback (PPF) [2, 4], while, in model-based algorithms such as linear quadratic (LQ) [3, 5] or model predictive control [6,7,8] (MPC), it allows the use of a relatively precise nominal model
A time-varying system behavior may detune the controller causing it to operate with suboptimal performance, but it may affect the stability of the closed-loop control system

Summary

Introduction

Undesirable mechanical and structural vibrations may often cause discomfort in humans and in certain engineering applications can even lead to catastrophic failure or other extreme consequences. When designing the algorithm support for AVC systems, a frequent assumption is that the controlled structure maintains its dynamic properties throughout the control procedure. This assumption enables the straightforward tuning of some controllers used in vibration attenuation like positive position feedback (PPF) [2, 4], while, in model-based algorithms such as linear quadratic (LQ) [3, 5] or model predictive control [6,7,8] (MPC), it allows the use of a relatively precise nominal model. One of the most important properties of self-reliant structural control systems is adaptivity, implying a degree of in situ intelligence [9]

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