High-accuracy adaptive vibrational control for uncertain systems

Attenuation of unwanted sound and vibrations is a key enabling technology in a vast array of aerospace and industrial control applications. In many defense, industrial, and medical applications, unwanted sound and vibrations which are primarily caused by rotating or reciprocating components are typically dominated by a number of harmonics. Effective suppression of these types of disturbances is essential to achieve accurate control. Examples include optical/laser jitter suppression, vibration reduction in helicopters, precise pointing/tracking of spacecraft, acoustic noise reduction in powertrain and aerial vehicles. In these and other applications, disturbance attenuation requires adaptation both in the estimation and rejection of the jitter source as well as the determination of the system itself. Vibrational disturbances often have multiple narrow-band components combined with broadband random noise which can be modeled as a sum of noise and some sinusoidal terms with unknown and possibly time-varying frequencies, phases, and amplitudes. Moreover, there always exists discrepancy between the actual dynamical system and its identified model. Therefore, a controller designed for attenuation of disturbances must be able to handle types of uncertainties. The proposed research focuses on output-feedback adaptive control of uncertain systems. The main objective is to design and analyze a robust adaptive control scheme which ensures globally asymptotic suppression of unknown unmeasurable disturbances with time-varying characteristics for some classes of uncertain plants. In almost all past work in this area, the problem of robustness with respect to plant unmodeled dynamics and bounded noise disturbances has not been adequately addressed and it is not clear that how the performance can be improved. In fact, most adaptive laws proposed in the literature for the problem of disturbance rejection were shown not to be robust back in the early 80's. These issues indicate the importance of establishing the robustness of these schemes with respect to inevitable modeling errors. ❧ In some applications, the plant model is almost linear and time-invariant (LTI) and can be identified off-line with relatively high accuracy over some frequency range. In the first step, we consider known single-input single-output (SISO) LTI plants in the presence of unknown unmodeled dynamics. We examine robust stability and performance of a robust adaptive control scheme and discuss the trade-off between robust stability and performance improvement and practical design considerations. We show that over-parameterization of the internal model of the disturbances provides structural flexibility to reduce the sensitivity of the plant output with respect to noise and provides further improvements. We demonstrate that pre-filtering of the plant input together with over-parameterization significantly improves the performance especially when the zeros of the internal model of the disturbance are close to those of the plant. We generalize the idea to multi-input multi-output (MIMO) LTI plants for both discrete-time and continuous-time systems and show that how the proposed control scheme designed for SISO plants can be modified to be applicable to MIMO plants with significant cross-couplings. ❧ In some other applications, the plant model may have large parametric uncertainties and/or the parameters may vary with time. For instance, change in flight condition in a flight vehicles, partial failure in some components of the system, or change in environment may lead to significant change in the plant model. Therefore, the controller must be able to adjust its parameters to counteract these variations and at the same time try to minimize the effect of vibrational disturbances. In such cases, both disturbance and plant model are unknown, ensuring the stability and performance of such a nonlinear and time-varying closed-loop system is very complicated as there is coupling and a nonlinear relation between the unknown parameters of the internal model of the disturbance and the unknown parameters of the plant. This makes separate estimations of the plant model and the internal model of the disturbance problematic. In spite of efforts done on this problem, the case of unknown plant model and unknown disturbance remains an open problem as no solution with guaranteed global stability has been yet proposed for practical implementation. We propose a practical solution to the problem of attenuation of unknown narrow-band disturbances acting on unknown linear systems in the presence of unstructured unmodeled dynamics.