This paper focuses on an electro-hydraulic servo system, which is derived from a shaking table. It proposes a control scheme based on a back propagation (BP) neural network, whose weights are trained by the particle swarm optimization (PSO) according to the fitness, which is determined by the input and the feedback signals. Each particle of PSO includes weights and thresholds of BP. The movement of each particle is adjusted by its local best-known position and the global best-known position in the searching space. With the update, a satisfactory solution can be achieved. In order to show the performance of the proposed control scheme, the designed network is also trained and tested by BP only. The comparisons between the PSO-BP and BP networks demonstrate that the PSO-BP one has better performance than that of BP, both in convergence speed and in convergence accuracy.

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Electro-hydraulic servo shaking table usually requires good control performance for acceleration replication. The poles of the electro-hydraulic servo shaking table are placed by three-variable control method using pole placement theory. The system frequency band is thus extended and the system stability is also enhanced. The phase delay and amplitude attenuation phenomenon occurs in electro-hydraulic servo shaking table corresponding to an acceleration sinusoidal input. The method for phase delay and amplitude attenuation elimination based on LMS adaptive filtering algorithm is proposed here. The task is accomplished by adjusting the weights using LMS adaptive filtering algorithm when there exits phase delay and amplitude attenuation between the input and its corresponding acceleration response. The reference input is weighted in such a way that it makes the system output track the input efficiently. The weighted input signal is inputted to the control system such that the output phase delay and amplitude attenuation are all cancelled. The above concept is used as a basis for the development of amplitude-phase regulation (APR) algorithm. The method does not need to estimate the system model and has good real-time performance. Experimental results demonstrate the efficiency and validity of the proposed APR control scheme.

Since there are nonlinearities in an electro-hydraulic servo shaking table, when the shaking table corresponds to sinusoidal shaking tests, its response contains higher harmonics, resulting in harmonic distortion and deteriorating the control performance. It needs to provide harmonic information for harmonic cancellation. The purpose of the paper is to develop an online acceleration harmonic identification algorithm for the shaking table. The unscented Kalman filter is applied to achieve this task. A nonlinear state space of the sinusoidal acceleration response is built for the unscented Kalman filter, which estimates the state of the nonlinear model, and the amplitude and phase of each harmonic, including the fundamental, can be directly decomposed from the identified state vector. The state transition equation is linear and the measurement equation is nonlinear. The efficiency and real-time performance of the developed acceleration harmonic identification are validated by simulation and experiment, in which the estimation error is further used to testify the estimation accuracy.

The acceleration output of an electro-hydraulic servo system corresponding to a sinusoidal input contains higher harmonics besides the fundamental input, because of complex nonlinearities occurring in the system. This causes harmonic distortion of the acceleration signal. The method for harmonic elimination based on adaptive notch filter is proposed here. The task is accomplished by generating a reference signal with a frequency that should be eliminated from the output. The reference input is filtered in such a way that it closely matches the harmonic. The filtered reference signal is added to the fundamental signal such that the output harmonic is cancelled leaving the desired signal alone. The weights of the adaptive filter are adjusted by the error between the input and the feedback acceleration to eliminate acceleration harmonic, creating an adaptive notch filter. The above concept is used as a basis for the development of an acceleration harmonic cancellation algorithm. Results of simulation and experiment on an electro-hydraulic servo shaking table demonstrate the efficiency and validity of the proposed control scheme.

Shaking tables play a vital role in mechanical environmental simulation. Sinusoidal shaking tests are usually applied to specimens for simulating periodic motions. Due to the nonlinearities in the electro-hydraulic servo shaking table, its sinusoidal acceleration response contains higher harmonics, which lower the system control performance. To cancel those harmonics, the harmonic information should be firstly known. The paper proposes an acceleration harmonic identification scheme by using the extended Kalman filter. A nonlinear state space model of the acceleration response is then built for the extended Kalman filter. The harmonic information, including the amplitude and phase of each harmonic, is directly derived from the estimated states. The features of the algorithm are that the state transition equation is linear and the measurement equation is nonlinear. It also inherits the advantages of the traditional linear Kalman filter. Both simulation and experimentation are carried out to validate its efficiency and accuracy. The online estimated harmonic information can provide a basis for the further harmonic cancellation.

Non-linearities commonly exist in an electro-hydraulic servo shaking table, causing acceleration harmonics distortion when the shaking table is excited by a sinusoidal acceleration signal, because its acceleration response includes higher harmonics, which lower the control performance for an electro-hydraulic servo shaking table. To cancel the harmonics in the system response, thus to improve the shaking table performance, we need to know about the harmonics information. An identification algorithm is developed here based on a Kalman filter for dynamically tracking the acceleration harmonics for the electro-hydraulic servo shaking table. A linear system in state space is modelled. The system acceleration response is applied as an observation value and is imported to the Kalman filter, which recursively estimates the state vector of the linear system. The amplitude and phase of each harmonic are calculated from the estimated state vector, and their estimated values are validated. A simulation example is presented and experiments were performed on the electro-hydraulic servo shaking table. Both results show a good estimation performance of the proposed acceleration harmonic identification algorithm.

For an electro-hydraulic servo shaking table, there are nonlinearities, which cause acceleration harmonic distortion when they corresponds to a sine acceleration excitation signal. The work here is to develop an acceleration harmonic identification algorithm by using the normalized least-mean-square (LMS) adaptive algorithm, whose weights are updated by the error between the acceleration response and the estimated acceleration signal. The input vector is generated by the reference harmonics and the [Formula: see text] phase shift. When the identification algorithm converges, the amplitude and phase of each harmonic can be computed from the weight vector. Experimental results show that the proposed harmonic identification has good real-time performance and a fast convergence rate, and it can identify harmonics on-line with high precision both in amplitude and in phase.