PPF Controller Research Articles

Frequency-Based Adaptive PPF Controller for Vibration Reduction of a Helicopter Shell Body

Frequency-Based Adaptive PPF Controller for Vibration Reduction of a Helicopter Shell Body

Applications of the integral equation method on nonlinear multi degree of freedom vibration systems

This paper compares the accuracy of the integral equation method and the multiple scales method in solving the amplitude equation of multi degree of freedom nonlinear vibration systems. We consider three examples: a two-degree-of-freedom stainless-steel beam system controlled by a saturation controller, a three-degree-of-freedom rotating compressor blade model and a four-degree-of-freedom horizontally supported Jeffcott-rotor system controlled by a PPF controller. The amplitude equations are obtained by applying the integral equation method and the method of multiple scales. The stability analysis is achieved based on the Floquet theory together with Routh–Hurwitz criterion. Furthermore, we modified the iterative procedure of the integral equation method to make the analytic approximate solution more accurate. Finally, the analyses show that in most cases, the analytical solutions obtained by the integral equation method are more excellent agreement with the numerical solutions than the most commonly used method of multiple scales. Therefore, the integral equation method is worth popularizing to obtain the approximate analytical solutions of the multi-degree-of-freedom nonlinear vibration system.

VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER

In this paper, the vibration reducing of the harmonically excited nonlinear system is presented via applying positive position feedback controller (PPF). The analytical results are obtained by applying the multiple-scale perturbation techniques (MSPT) up to second-order approximations. The frequency response equation (FRE) is studied to test the be havior of the steady state solutions near the simultaneous resonances. The effects of the several parameters and the behavior of the system at resonance case are investigated to illustrate the optimum working conditions for the PPF controller. The stabilit y analysis for the uncontrolled system is investigated by applying the phase portrait technique. Moreover, numerical simulation is used to compare between time-history and the analytical solution. The analytical and numerical solutions are compared to show the validity of the results. Finally, a comparison with the available results in the literature is presented

지능구조물의 진동 억제를 위한 적응 양변위 되먹임 제어기 개발

In this study, an adaptive positive-position feedback control (PPF) algorithm was developed for vibration suppression of smart structures equipped with piezoceramic sensor and actuator. The PPF control is capable of selectively increasing the damping of the target mode by tuning the filter frequency of the PPF controller to the natural frequency of the target mode. However, the performance of the PPF control can be deteriorated if the filter frequency of the PPF controller is not accurately tuned to the natural frequency of the target structure. Hence, the natural frequencies of a smart structure should be determined a priori to the application of the PPF control either theoretically or experimentally. In order to solve this problem, the frequency estimation algorithm that can calculate the major frequency of the structure was combined with the PPF control, thus realizing the adaptive PPF control. The performance of the proposed adaptive PPF control was validated experimentally by using a beam structure consisting of a piezoceramic sensor and an actuator. Experimental results show that the frequency could be accurately estimated in real time, and the vibrations of the structure were effectively suppressed.

Modal sensing and control of paraboloidal shell structronic system

Abstract Paraboloidal shells of revolution are commonly used as important components in the field of advanced aerospace structures and aviation mechanical systems. This study is to investigate the modal sensing behavior and the modal vibration control effect of distributed PVDF patches laminated on the paraboloidal shell. A paraboloidal shell sensing and control testing platform is set up first. Frequencies of lower order modes of the shell are obtained with the PVDF sensor and compared with the previous testing results to prove its accuracy. Then sensor patches are laminated on different positions (or different sides) of the shell and tested to reveal the relation between the sensing behaviors and their locations. Finally, a mathematical model of the structronic system is built by parameter identifications and the transfer function is derived. Independent and coupled modal controllers are designed based on the pole placement method and modal vibration control experiments are performed. The amplitude suppression ratio of each mode controlled by the pole placement controller is calculated and compared with the results obtained by using a PPF controller. Advantages of both methods are concluded and suggestions are given on how to choose control algorithm for different purpose.

Performance characteristics of a real-power viscoelastic isolation system under delayed PPF control and base excitation

The paper mainly presents the dynamical characteristics of a base-excited viscoelastic isolation system with real-power geometric nonlinearities under a delayed PPF controller. This controller is coupled to the main system with 1:1 internal resonance. Firstly, the perturbation method of multiple scales is adopted to explicitly find the coupled relationship of the frequency response equations. The results demonstrate that under over-linear restoring force, the amplitude–frequency responses of the viscoelastic isolation system are of the hardening type, which only appears on the right branch of the double-peak response. In this respect, increasing the detuning parameter of the controller results in the appearance of frequency island phenomenon on the right branch of the double-peak response, while the amplitude of the controller degenerates into the traditional single-peak response along with the frequency island. Then, it is worth noting that the vibration can be suppressed effectively by the viscoelastic damping parameters. Furthermore, eight types of interesting dynamical response phenomena are found with the change in time delays under different excitation amplitudes. To this end, the stability analysis, showing the performance of the controller strategy, is carried out by combining the response characteristics. Finally, from the perspective of suppressing the peak amplitude and maintaining the resonance stability, the suitable feedback gains and time delays are determined by means of frequency responses as well as stability conditions.

Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach

This paper introduces Nonlinear Modified Positive Position Feedback (NMPPF) control approach for nonlinear vibration suppression at primary resonance. Nonlinearity in the system is due to large deformations caused by high-amplitude disturbances, while this control approach is applicable to all types of nonlinearities in resonant structures. NMPPF controller consists of a resonant second-order nonlinear compensator, which is enhanced by a lossy integrating compensator. The two compensators create a combination of exponential and periodic control inputs, which needs innovative time scaling for using the Method of Multiple Scales to obtain the analytical solution of the closed-loop system. The results of the analytical solution for the closed-loop NMPPF controller are presented and compared with the result of the conventional PPF controller. Effects of the control parameters on the system response are comprehensively studied by parameter variations. The approximate solution is then verified using numerical simulations. According to the results, the NMPPF controller provides a higher level of suppression in the overall frequency domain, as the peak amplitude at the neighborhood frequencies of the primary mode is reduced by 44 %, compared to the PPF method. The tunable control parameters also give more flexibility to create the expected type of system response.

Analysis of smart beams with piezoelectric elements using impedance matrix and inverse Laplace transform

A comprehensive study on smart beams with piezoelectric elements using an impedance matrix and the inverse Laplace transform is presented. Based on the authors’ previous work, the dynamics of some elements in beam-like smart structures are represented by impedance matrix equations, including a piezoelectric stack, a piezoelectric bimorph, an elastic straight beam or a circular curved beam. A further transform is applied to the impedance matrix to obtain a set of implicit transfer function matrices. Apart from the analytical solutions to the matrices of smart beams, one computation procedure is proposed to obtained the impedance matrices and transfer function matrices using FEA. By these means the dynamic solution of the elements in the frequency domain is transformed to that in Laplacian s-domain and then inversely transformed to time domain. The connections between the elements and boundary conditions of the smart structures are investigated in detail, and one integrated system equation is finally obtained using the symbolic operation of TF matrices. A procedure is proposed for dynamic analysis and control analysis of the smart beam system using mode superposition and a numerical inverse Laplace transform. The first example is given to demonstrate building transfer function associated impedance matrices using both FEA and analytical solutions. The second example is to verify the ability of control analysis using a suspended beam with PZT patches under close-loop control. The third example is designed for dynamic analysis of beams with a piezoelectric stack and a piezoelectric bimorph under various excitations. The last example of one smart beam with a PPF controller shows the applicability to the control analysis of complex systems using the proposed method. All results show good agreement with the other results in the previous literature. The advantages of the proposed methods are also discussed at the end of this paper.

Vibration Suppression of a Flexible Structure

Abstract This work addresses the solution to the problem of active vibration suppression of a cantilever beam using piezoelectric actuation. For this purpose, we are taking advantage of the effectiveness of the positive position feedback control strategy (PPF) in order to control first mode vibrations of the analyzed beam. This control technique is well-known in the literature as a modal control method for vibration attenuation. The PPF controller accomplishes its best performance if tuned properly to the characteristics of the structure to be controlled. According to this we are going to realize the modal analysis of the cantilever beam utilizing the finite element method in Ansys to determine the structural frequency corresponding to the first mode, which is used as PPF controller frequency. On the other hand, we shall obtain the state-space representation of the cantilever beam using the subspace identification method in frequency domain applying the fast fourier transformation (FFT). Furthermore, we will simulate the discrete-time PPF controller using Matlab/Simulink. Lastly, the simulink designed discrete-time PPF controller will be tested using an xPC Target real-time system.

능동동조질량감쇠기와 수정 PPF 제어기를 이용한 구조물의 능동진동제어

This paper is concerned with the active vibration control of building structure by means of the active tuned mass damper and the modified positive position feedback controller. To this end, one-degree-of-freedom spring-mass-damper system equipped with ATMD is considered. The stability condition for the addressed system when applying the proposed PPF controller is derived by Routh-Hurwitz stability criterion. The stability condition shows that the modified PPF controller is absolutely stable if the controller gain is positive. so that the modified PPF controller can be used without difficulty. Theoretical study shows that the modified PPF controller can effectively suppress vibrations as the original PPF controller does in smart structure applications. To investigate the validity of the modified PPF controller, a simple experimental structure with an ATMD system driven by DC motor was built. The modified PPF control algorithm was implemented on Atmel 128 microcontroller. The experimental result shows that the modified PPF controller can also suppress vibrations for the real structure.

적응형 PPF 제어기를 이용한 지능구조물의 실시간 능동진동제어

This research is concerned with the development of a real-time adaptive PPF controller for the active vibration suppression of smart structure. In general, the tuning of the PPF controller is carried out off-line. In this research, the real-time learning algorithm is developed to find the optimal filter frequency of the PPF controller in real time and the efficacy of the algorithm is proved by implementing it in real time. To this end, the adaptive algorithm is developed by applying the gradient descent method to the predefined performance index, which is similar to the method used popularly in the optimization and neural network controller design. The experiment was carried out to verify the validity of the adaptive PPF controller developed in this research. The experimental results showed that adaptive PPF controller is effective for active vibration control of the structure which is excited by either impact or harmonic disturbance. The filter frequency of the PPF controller is tuned in a very short period of time thus proving the efficiency of the adaptive PPF controller.