Ehsan Omidi

Vibration control of collocated smart structures using H ∞ modified positive position and velocity feedback

In this paper, H∞ modified positive position feedback (HMPPF) and H∞ modified positive velocity feedback (HMPVF) controllers are developed as two innovative controllers for active vibration reduction in flexible collocated structures. The controllers use the concept of modified positive feedback and are enhanced by the H∞ feedback design to provide effective vibration suppression of multiple modes. An aluminum cantilever beam is used to experimentally evaluate the performance of the two controllers. The objective of the HMPPF controller is to suppress vibration displacement when all of the fundamental modes are excited. In this case which considers the first three modes of the flexible structure, overall vibration displacement is reduced to 38% of the uncontrolled value. The HMPVF, on the other hand, uses the control energy to reduce the vibration velocity to the lowest possible value. Vibration velocity amplitude using the HMPVF approach was reduced more than displacement, which makes this controller more effective for fatigue failure prevention purposes.

Hybrid Positive Feedback Control for Active Vibration Attenuation of Flexible Structures

A new controller is introduced in this paper as a novel method for active vibration suppression in flexible structures. The hybrid positive feedback (HPF) uses a second- and a first-order compensator that are fed by the displacement and velocity feedbacks, respectively. Parallel pairs of the HPF controller are implemented when suppression in multimode condition is issued. Since the controller uses two gains for each pair of the actuator/sensor patch for each mode, a suitable gain optimization method has to be used to ensure the optimum performance. To this end, H2 and H∞ optimization approaches are utilized. For validation purposes, the controller is verified numerically and experimentally for vibration control of a cantilever beam. System identification is performed, then closed-loop system responses to simultaneous multimode and swept frequency excitations are obtained. According to the results, the HPF controller has a superior performance compared to the conventional method of positive position feedback. Vibration displacement amplitudes were reduced by more than 85% relative to the uncontrolled state. The best performance was achieved by the H2-optimized HPF, as the net value for vibration displacement amplitude reduction in the multimode condition was 90% of the uncontrolled amplitude.

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay.

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound.

Implementation of modified positive velocity feedback controller for active vibration control in smart structures

This paper introduces the Modified Positive Velocity Feedback (MPVF) controller as an alternative to the conventional Positive Position Feedback (PPF) controller, with the goal of suppressing unwanted resonant vibrations in smart structures. The MPVF controller uses two parallel feedback compensators working on the fundamental modes of the structure. The vibration velocity is measured by a sensor or state estimator and is fed back to the controller as the input. To control n-modes, n sets of parallel compensators are required. MPVF controller gain selection in multimode cases highly affects the control results. This problem is resolved using the Linear Quadratic Regulator (LQR) and the M-norm optimization method, which are selected to form the desired performance of the MPVF controller. First, the controller is simulated for the two optimization approaches, and then, experimental investigation of the vibration suppression is performed. The LQR-optimized MPVF provides a better suppression in terms of vibration displacement. The M-normoptimized MPVF controller focuses on modes with higher magnitudes of velocity and provides a higher level of vibration velocity suppression than LQR-optimized method. Vibration velocity attenuation can be very important in preventing fatigue failures due to the fact that velocity can be directly related to stress.

Active Vibration Control of Resonant Systems via Multivariable Modified Positive Position Feedback

One of the predominant difficulties in the theory of distributed structure control systems comes from the fact that these resonant structures have a large number of active modes in the working band-width. Among the different methods for vibration control, Positive Position Feedback (PPF) is of interest, which uses piezoelectric actuation to overcome the vibration as a collocated controller. Modified Positive Position Feedback (MPPF) is later presented by adding a first-order damping compensator to the conventional second-order compensator, to have a better performance for steady-state and transient disturbances. In this paper, Multivariable Modified Positive Position Feedback (MMPPF) is presented to suppress the unwanted resonant vibrations in the structure. This approach benefits the advantages of MPPF, while it controls larger number vibration modes. An optimization method is introduced, consisting of a cost function that is minimized in the area of the stability of the system. LQR problem is also used to optimize the controller performance by optimized gain selection. It is shown that the LQR-optimized MMPPF controller provides vibration suppression in more efficiently manner.© 2013 ASME

Novel Hybrid Positive Feedback control for active vibration suppression in flexible structure

A new controller is introduced in this paper as a novel approach toward active vibration suppression in flexible structures. Hybrid Positive Feedback (HPF) uses a second- and a first-order compensator that are fed by displacement and velocity feedbacks, respectively. Parallel pairs of the HPF controller are implemented when suppression in multimode condition is issued. Since the controller uses two gains for each pair of actuator/sensor patched of each mode, an optimized gain selection task is essential. Hence, H2 and ℋ∞ optimization approaches are utilized to provide the best level of suppression using the HPF controller. Numerical simulations and a set of experiments are implemented to evaluate the performance of the controller. Comparison of the HPF controller result with the Positive Position Feedback (PPF) method demonstrates the superiority of the new method. HPF controller using either of the optimization methods attenuates the vibration displacement amplitude to at least 85% of the uncontrolled amplitude. However, best result is achieved using the ℋ∞-optimized process as the net value of vibration displacement amplitude caused by a multimode disturbance is reduced by 90% of the uncontrolled displacement amplitude.

Nonlinear Vibration Control of Flexible Structures Using Nonlinear Modified Positive Position Feedback Approach

A new Nonlinear Modified Positive Position Feedback (NMPPF) controller is proposed in this paper to suppress the nonlinear resonant vibrations in flexible structures. The NMPPF uses a nonlinear second-order feedback compensator to overcome the vibrations at exact primary resonance frequency, and a first-order integrating term to lower the remaining peak amplitudes in the frequency domain. For the closed-loop system, an innovative implementation of the Method of Multiple Scales is employed to obtain the modulation equations. Results demonstrate the superior performance of the NMPPF controller compared to the conventional approach i.e. Positive Position Feedback (PPF), as the suppression performance is improved by 62% in the peak amplitude reduction. The presented parameter analysis of the NMPPF controller also proposes the optimal controller parameters to provide the highest suppression level in the nonlinear oscillatory system.© 2014 ASME

Spatial Vibration Control of Thin Beams Using Multimode Modified Positive Position Feedback

Spatial multimode resonant vibration suppression using Modified Positive Position Feedback (MPPF) approach is presented in this paper. Spatial implementation of the MPPF controller considers vibration attenuation in the whole structure, rather than on a limited number of local control points. This approach utilizes spatial norm minimization of H2 and H∞, which considers vibration amplitude of all points on the structure in a model-based design. The designed controller is then evaluated using a clamped-clamped (c-c) and a cantilever beam as the test platforms. According to the numerical simulations and experimental results, spatial MPPF controller using both norm minimization techniques provides a high level of vibration suppression all over the structure, and for all active resonant modes. The MPPF-H∞ controlled system has a smoother response in the frequency domain, which is more preferable when the closed-loop system experiences a frequency sweep disturbance. At exact resonant frequency however, experimental results confirm a better suppression performance using the spatial MPPF-H2 method on different points of both beam structures.Copyright

Active vibration control of structures using a leader–follower-based consensus design:

This paper proposes a new leader–follower-based consensus vibration controller to actively suppress unwanted oscillations in distributed-parameter flexible structures. Actuation and sensing is performed via piezoelectric layers in a collocated sense. The actuator/sensor patches for the vibration control system are considered to collaborate in a network, and follow a virtual leader which is accessible to all agents. Hence, a vibration controller law is defined, to remove disagreement between agents and force the agents to follow the virtual leader. The proposed approach is an observer-based design, in which an optimal consensus state estimator is initially designed. Stability of the closed-loop system is investigated and the optimality conditions of the system are derived. Although the designed vibration controller could be implemented for suppression tasks in different distributed-parameter systems, a flexible clamped-clamped beam is used here for equation derivation and numerical performance verification. According to the results, the optimal observer estimates the system states in a finite time, as expected, and the vibration controller suppresses unwanted oscillations, either in resonant or arbitrary form, to a much lower level; while the disagreement between agents converges to zero. Additionally, suppression performance and robustness of the controller to failure in control system elements is investigated in comparison with a conventional positive position feedback controller, and its superiority is illustrated and discussed.

Consensus-based multi-piezoelectric microcantilever for scanning probe microscopy

A new multi-piezoelectric microcantilever sensor is introduced in this article for replacing laser sensors in atomic force microscopes. This microcantilever consists of multiple piezoelectric layers over its surface, and a consensus algorithm is designed to provide a robust and accurate estimation of the deflections at the tip of the microcantilever. The dynamic equation set of the microcantilever is developed first and then the consensus observer is designed. A set of Riccati equations is used to obtain the optimal gains for the observer, and the robustness of the microcantilever is considered by designing a H∞ norm constraint. A set of numerical simulations is conducted to evaluate the performance of the microcantilever. Results show that the consensus-based multi-piezoelectric microcantilever can successfully provide an accurate estimation of the deflections at the tip of the microcantilever. It is also shown that the robustness of the design can positively improve the estimation performance in the presence of noise. Additionally, a comparison with a single-layered design shows the advantages of the new sensor.