Observer-based repetitive model predictive control in active vibration suppression

Abstract

In this paper, an observer-based feedback/feedforward model predictive control (MPC) algorithm is developed for addressing the active vibration control (AVC) of lightly damped structures. For this purpose, the feedback control design process is formulated in the framework of disturbance rejection control (DRC) and a repetitive MPC is adapted to guarantee the robust asymptotic stability of the closed-loop system. To this end, a recursive least squares (RLS) algorithm is engaged for online estimation of the disturbance signal, and the estimated disturbance is feed-forwarded through the control channels. The mismatched disturbance is considered as a broadband energy bounded unknown signal independent of the control input, and the internal model principle is adjusted to account for its governing dynamics. For the sake of relieving the computational burden of online optimization in MPC scheme, within the broad prediction horizons, a set of orthonormal Laguerre functions is utilized. The controller design is carried out on a reduced-order model of the experimental system in the nominal frequency range of operation. Accordingly, the system model is constructed following the frequency-domain subspace system identification method. Comprehensive experimental analyses in both time-/frequencydomain are performed to investigate the robustness of the AVC system regarding the unmodeled dynamics, parametric uncertainties, and external noises. Additionally, the spillover effect of the actuation authorities and saturation of the active elements as two common issues of AVC systems are addressed.KEYWORDS disturbance estimation, model predictive control, orthonormal basis functions, piezoelectric material, vibration attenuation | INTRODUCTIONModel predictive control (MPC) is an optimization-based method in which, the control inputs are obtained by solving a set of finite-horizon optimal control problems successively over the sampling instants. The optimal control formulation of the MPC explicitly takes into account model-based predictions of the controlled system trajectories. The obtained solutions of the optimal control problems are concatenated in a receding horizon framework, to construct the MPC feedback law. By the advances of embedded computer processors along with the enhanced optimization solvers, the MPC methods are appearing more and more in the emerging industrial applications. [1] In comparison with the other industrial control

Robust Linear Output Regulation Using Extended State Observer

“…In many engineering systems, only the dominant frequencies of the disturbances can be obtained via time and/or frequency domain identification methods (see, for example, [8]). In such systems, one can embed the known dominant frequencies into the system (2) and model the corresponding disturbance approximation error into the term, (.).…”

“…For any given matrices and , there exist unique matrices and satisfying (8) if and only if the following assumption holds.…”

“…Both control signals are approximately the same; however, there is a high-frequency component in the control input of our controller. This component is caused by the internal model property of our controller which embeds the known frequencies of the reference/disturbances to learn their behavior [8]. In order to assess the performance of the ESO, the estimated state variables of the plotter system are given in Figure 5.…”

“…For example, in many structural vibration control problems, the main source of the disturbance is the unmodeled higher order modes. Even though the dominant higher order modes can be obtained via suitable system identification methods, a comprehensive dynamic model for the disturbances is not feasible [8]. As another example, in many mechanical and electromechanical systems, parametric 2 Mathematical Problems in Engineering uncertainty, friction, and nonlinear effects bring about statedependent disturbances that are not guaranteed to belong to the solution space of any particular dynamic system [9].…”

Controlling uncertain nonlinear structural vibrations of moving continuum system by embedding a vibration monitoring unit to feedback algorithm

“…Considering the fact that real mechanical systems always contain a certain level of flexibility, controller design and verification based on solely rigid model of a system may not lead to similar performance in real applications. Thus, the control problem of vibrational systems has become of great interest in recent studies 1–18 . These investigations are generally categorized into analytical and numerical approaches.…”